Tunnel Electron Radiation on Recombination Center
|
|
- Horatio Bradford
- 7 years ago
- Views:
Transcription
1 Tunnel Electron Radiation on Recombination Center, P.A. Golovinski, A.A. Drobyshev ) Moscow Institute of Physics and Technology (State University), Moscow, Russia ) Voronezh State University of Architecture and Civil Engineering, 946, Voronezh, Russia The photorecombination radiation on a neighbor center of an electron ionized in the nonlinear tunneling regime is discussed. In the framework of the active electron model an analytical solution of the problem has been obtained. The analytical solution for distribution of the radiation energy spectrum has been derived both for one and three dimension problems. The optimal parameters of the field and the distance between quantum wells for a process of effective photorecombination with a broad spectrum have been formulated. Introduction. During the past decade the vast efforts have been concentrated on the dynamical electron effects of the high harmonic generation in the focus of the femtosecond and attosecond laser pulses [-]. The nonlinear ionization of atoms with the following acceleration of the electrons by a monochromatic low frequency laser field with high intensity can result in the recombination of an electron in the nearest capture centers and is accompanied by radiation of the short time electromagnetic pulses. In this work we discuss radiation of an electron, tunneled from the bound quantum state under the action of a low frequency electric component of the laser field F( F cos( ( F is the amplitude of an electric strength, is the laser field frequency), in the process of the next center recombination. The low frequency limit for a nonlinear ionization from the state with the energy E is realized when the Keldysh s parameter / F [4]. In i E i this limiting case the ionization is a quasisteady process, and it mainly occur near the amplitude value F of the laser field [5]. The validity of the model is confirmed golovinski@bk.ru
2 by applicability of the ADK formula [6] to the description of nonlinear atom ionization. We describe electron radiation as a three step process: nonlinear ionization, acceleration in the laser field, and photorecombination to the final bound state [7, 8]. The majority of modern experiments for the high harmonic generation are in a good agreement with the Corcum s rescattering model [9, ]. According to this model the radiation is a result of the electron, driving by alternating laser field, is returning to the initial atom. In some cases an electron comes back to the parent atom with the enough high energy and produces photons during the recombination. The probability of the process at a low frequency limit tends to zero as a result of wave packet dispersion when the time of a comeback is too large for efficient interaction with the parent center []. However, another process accompanied by photorecombination is possible and may be more efficiently. The laser field can be assumed to be quasi static, if the oscillation amplitude F / be greater than the distance R between two centers. We use atomic units e m throughout the paper. The collision energy of the electron then is estimated as p / RF. The recombination probability tends to maximum value p ~ / a, where a is a characteristic size of the final state wave function. Hence, the maximum of the radiation intensity is achieving at the distance ) R ~ (Fa, and for a ~, I W/cm the corresponding optimal distance R 5 a.u.. Active electron model. We consider the active electron model based on the Feinman s propagation function []. The figure demonstrates a scheme of photorecombination for the tunneling electron. To describe the process we start from the Schrödinger s equation i H ( x, W ( x,, () t where H is the Hamiltonian of an electron in the external field, and
3 W ( x, W ( x) e it, W ( x) i V / ( e r) is the operator of the one photon spontaneous emission in the dipole approximation []. Here is the spontaneous photon frequency, e is its polarization, V is the quantization volume. () Fig.. The scheme of photorecombination for the tunneling electron. The exact solution to the Schrödinger s Eq. () has to satisfy a linear homogeneous integral equation of the form ( x, i d x G( x, t; x, t) i ( x, t), t t, () where G x, t ; x, t ) is the propagator or the Green s function, and the integration ( extends over the whole space. The probability amplitude for transition from the initial state ( x, to the final state ( x, has the form i S if f * f ( i i d x d x x, G( x, t; x, t ) ( x, t ). (4) The Green s function for the time independent Hamiltonian (in the static fields) has eigenmod expansion G * ( x, t; x, t x ) i ( t t ) exp( ie ( t t )) ( x) ( ), (5) where n (x ) are is the eigenfunctions of the operator H. Then, we have S if d * i( E f ) t x dt d x ( ) f x e W ( x) G ( x, t; x, t) i ( x, t ). (6)
4 The analytical approach to the high harmonic generation in the delta potential model has been developed in [4], where the three step approximation has been substantiated. We operate with this approximation and represent the wave function of the active electron i d x G x, t ; x, t ) ( x, t ) as a sum of the bound state ( i exp( -iei i ( x) and the wave packet c ( x, in the continuum [5], i.e. x, t ) exp( -ie t ) ( x ) + ( x, ). (7) ( i i c t The propagation of this wave packet is described by the relation x, t ) w( F ) G( x, t,,), (8) c( x where G x, t,,) is the Green s function of the electron in a homogeneous ( x electric field F, x is the turn point coordinate in the static potential at the moment t. The expression for the S -matrix element we can rewrite in terms of the retarded Green s function for electric field ) ~ ) ~ * G x, t, x,) i ( t ) exp( ie t ( x ( ), (9) ( x where ~ ( ) is the electron wave function in a uniform electric field, as follows x S if w * i( E f ) t ( F ) d x dt f ( x) e W ( x ) G( x, t, x,). () We, mostly, fully took into account the influence of the electric field on the continuum spectrum states. The summation in the Eq. (9) is replaced by the integration over continuum quantum numbers. After substitution of the Eq. (9) into the Eq. () we get 4 S fi * w( F ) ( x) W ( x) ~ ( x) ~ ( x) E f E t. () f This equation contains the conservation energy law in the form of the delta function. The probability of transition per unit of time can be obtained by additional summation over final states. In this case it is a number of final states dn for the radiated photons with the momentum in the interval ( p, p dp), the polarization e in some solid angle d, and the volume V :
5 5 Vp dp d dn. () c ( ) The distribution density for the radiation energy over frequency we write down in the form 4 4 d d w( F ) r. () c This formula can be applied to the problems of an arbitrary dimension. Two quantum wells. As an application of the general formalism we consider a system with two parabolic quantum wells, which is the one dimensional problem. The sum in the Eq. () is changed to the integration over the energy, and G ( x, t, x,) de exp( ie E ( x) E ( x ), (4) where E (x ) are normalized wave functions of the electron in a homogeneous electric field expressed in terms of the Airy function [8]: u E ( x) Ai( q),ai( q) uq du F cos, (5) q x E / F, F /. The Fourier components of the dipole matrix element are D w ( F f E f E f x ) ( x) x ( x) ( ). (6) The final state we take in the form of wave function for the quantum linear oscillator [9] / / exp ( x ) / ( x), (7) f x where x is a recombination center of the electron. The probability of ionization, per half of period of the external laser field oscillation T / /, exponentially depends on the electric strength: w F 4 exp E i F /. (8)
6 The complete expression for the dipole matrix element results through Eq.(6) Eq. (8): D Ai / F 4 exp E F Ai x E / F x exp ( x x ) / dx, i / q q x E / F. (9) The coordinate x Ei / F corresponds to the return point. The Eq. (9) in combination with the Eq. () allows us to calculate the spectrum of the electron photorecombination. The main influence factor of modulation is the function ( E E ) /( F i Ai ). The integral in the Eq. (9) can be evaluated asymptotically for large arguments of the Airy function. In the figure two photorecombination spectrums are plotted for different intensities. The comparison of them shows decreasing of the intensity and increasing the number of oscillations in the spectrum. 6 Fig.. The dependence of the recombination spectrum from the intensity of a laser field. The distance between centers of ionization and recombination is 5 а.u., the intensity of a laser field I W/cm (а), I W/cm (b).
7 7 Fig.. The dependence of a maximum of the intensity of the photorecombination radiation from the distance between the centers of ionization and recombination for the intensity of the CO laser I W/cm. The figure demonstrates the dependence of the photorecombination efficiency as a function of the distance between two attraction centers. The spectrum maximum lies at wavelength radiation. RF E f. The increasing R leads to the shorter Conclusions. The measurements of the recombination radiation allow one to estimate ionization potential or the distance between two centers. Practically the same scheme can be applied to the problem with two quantum dots, taking them as initial and final recombination centers. Obviously, the intensity of photorecombination in three dimension case strongly depends on the angle between polarization and the axis of symmetry for a system of the two quantum dots. [] I. J. Sola, E. Mevel, L. Elouga, et. al., Nature Phys., 9 (6). [] P. B. Corcum, F. Krausz, Nature Phys., 8 (7). [] E. A. Volkova, A.M. Popov, O. V. Tikhonova, Pis ma v ZETP 94, 559 ().
8 8 [4] A. Baz, Ya. Zeldovich, A. Perelomov, Scattering Reactions and Decay in Nonrelativistic Quantum Mechanics, Israel program for scientific translations, Jerusalem, 969. [5] Delone N.B., V.P. Krainov, Multiphoton Processes in Atoms, Springer-Verlag, Berlin, 994. [6] M.V. Ammosov, Delone N.B., V.P. Krainov, Sov. Phys. JETP 64, 9 (986). [7] S. L. Chin, P. A. Golovinski, J. Phys. B.: At. Mol. Opt. Phys. 8, 55 (995), [8] M. Yu. Kuchiev, V. N. Ostrovsky, Phys. Rev. A 6, (999). [9] P. B. Corkum, Phys. Rev. Lett. 7, 994 (99). [] K. C. Kulander, J. Cooper, K. J. Schafer, Phys. Rev. A 5, 56 (995). [] P. A. Golovinski, Laser Phys., 8 (99). [] J. D. Bjorken, S. D. Drell. Relativistic Quantum Theory, V., NY.: MCH, (964). [] A.S. Davydov, Quantum Mechenics, Pergamon Press, Oxford, 976. [4] M. V. Frolov, N. L. Manakov, T. S. Sarantseva, et. al., J. Phys. B.: At. Mol. Opt. Phys. 4, 56 (9). [5] W. Becker, S. Long, J. K. McIver, Phys. Rev. A 5, 54 (994). [6] L.D. Landau, E.M. Lifshitz, Classical Theory of Fields, 4 rd ed., Pergamon, Oxford, 975. [7] R. W. Kelsall, I. W. Hamley, Nanoscale Science and Technology, Geoghegan, John Wiley and Sons, 5. [8] M. Abramowitz, I. A. Stegun, Handbook of mathematical functions, National Bureau of Standards, Washington, 97. [9] L.D. Landau, E.M. Lifshitz, Quantum Mechatics: Nonrelativistic Theory, rd ed., Pergamon, Oxford, 977. [] S. L. Chin, Y. Liang, S. Augst et. al., J. of Nonlinear Opt. Phys. & Mat. 4, 667 (995). [] P. A. Golovinski, E. M. Mikhailov, Phys. Scr. 6, 4 (). [] A. N. Zheltukhin, A. N. Manakov, A. V. Flegel, M. V. Frolov, Pis ma v ZETP 94, 64 ().
Raman Scattering Theory David W. Hahn Department of Mechanical and Aerospace Engineering University of Florida (dwhahn@ufl.edu)
Introduction Raman Scattering Theory David W. Hahn Department of Mechanical and Aerospace Engineering University of Florida (dwhahn@ufl.edu) The scattering of light may be thought of as the redirection
More information- thus, the total number of atoms per second that absorb a photon is
Stimulated Emission of Radiation - stimulated emission is referring to the emission of radiation (a photon) from one quantum system at its transition frequency induced by the presence of other photons
More informationThe Role of Electric Polarization in Nonlinear optics
The Role of Electric Polarization in Nonlinear optics Sumith Doluweera Department of Physics University of Cincinnati Cincinnati, Ohio 45221 Abstract Nonlinear optics became a very active field of research
More informationNumerical Model for the Study of the Velocity Dependence Of the Ionisation Growth in Gas Discharge Plasma
Journal of Basrah Researches ((Sciences)) Volume 37.Number 5.A ((2011)) Available online at: www.basra-science -journal.org ISSN 1817 2695 Numerical Model for the Study of the Velocity Dependence Of the
More informationFractional Revival of Rydberg Wave Packets in Twice-Kicked One-Dimensional Atoms
Vol. 0 0) ACTA PHYSICA POLONICA A No. 3 Fractional Revival of Rydberg Wave Packets in Twice-Kicked One-Dimensional Atoms S. Chatterjee Department of Physics, Bidhannagar College, EB-, Sector-, Salt Lake,
More informationFLAP P11.2 The quantum harmonic oscillator
F L E X I B L E L E A R N I N G A P P R O A C H T O P H Y S I C S Module P. Opening items. Module introduction. Fast track questions.3 Ready to study? The harmonic oscillator. Classical description of
More informationThe Quantum Harmonic Oscillator Stephen Webb
The Quantum Harmonic Oscillator Stephen Webb The Importance of the Harmonic Oscillator The quantum harmonic oscillator holds a unique importance in quantum mechanics, as it is both one of the few problems
More informationThree Pictures of Quantum Mechanics. Thomas R. Shafer April 17, 2009
Three Pictures of Quantum Mechanics Thomas R. Shafer April 17, 2009 Outline of the Talk Brief review of (or introduction to) quantum mechanics. 3 different viewpoints on calculation. Schrödinger, Heisenberg,
More informationBroadband THz Generation from Photoconductive Antenna
Progress In Electromagnetics Research Symposium 2005, Hangzhou, China, August 22-26 331 Broadband THz Generation from Photoconductive Antenna Qing Chang 1, Dongxiao Yang 1,2, and Liang Wang 1 1 Zhejiang
More informationInfrared Spectroscopy: Theory
u Chapter 15 Infrared Spectroscopy: Theory An important tool of the organic chemist is Infrared Spectroscopy, or IR. IR spectra are acquired on a special instrument, called an IR spectrometer. IR is used
More informationarxiv:1111.4354v2 [physics.acc-ph] 27 Oct 2014
Theory of Electromagnetic Fields Andrzej Wolski University of Liverpool, and the Cockcroft Institute, UK arxiv:1111.4354v2 [physics.acc-ph] 27 Oct 2014 Abstract We discuss the theory of electromagnetic
More informationAssessment Plan for Learning Outcomes for BA/BS in Physics
Department of Physics and Astronomy Goals and Learning Outcomes 1. Students know basic physics principles [BS, BA, MS] 1.1 Students can demonstrate an understanding of Newton s laws 1.2 Students can demonstrate
More informationN 1. (q k+1 q k ) 2 + α 3. k=0
Teoretisk Fysik Hand-in problem B, SI1142, Spring 2010 In 1955 Fermi, Pasta and Ulam 1 numerically studied a simple model for a one dimensional chain of non-linear oscillators to see how the energy distribution
More informationIntroduction to Schrödinger Equation: Harmonic Potential
Introduction to Schrödinger Equation: Harmonic Potential Chia-Chun Chou May 2, 2006 Introduction to Schrödinger Equation: Harmonic Potential Time-Dependent Schrödinger Equation For a nonrelativistic particle
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives
Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring
More informationd d Φ * Φdx T(B) Barrier (B ) : Vo = 5, a = 2 Well (W ) : Vo= -5, a = 2 0.0 0 2 4 6 8 10 12 14 16 18 20 ENERGY (E)
Quantum Mechanical Transmission with Absorption S. MAHADEVAN, A. UMA MAHESWARI, P. PREMA AND C. S. SHASTRY Physics Department, Amrita Vishwa Vidyapeetham, Coimbatore 641105 ABSTRACT Transmission and reflection
More informationWaves - Transverse and Longitudinal Waves
Waves - Transverse and Longitudinal Waves wave may be defined as a periodic disturbance in a medium that carries energy from one point to another. ll waves require a source and a medium of propagation.
More informationAPPLIED MATHEMATICS ADVANCED LEVEL
APPLIED MATHEMATICS ADVANCED LEVEL INTRODUCTION This syllabus serves to examine candidates knowledge and skills in introductory mathematical and statistical methods, and their applications. For applications
More informationAnalysis of Electromagnetic Propulsion on a Two-Electric-Dipole System
Electronics and Communications in Japan, Part 2, Vol. 83, No. 4, 2000 Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J82-C-I, No. 6, June 1999, pp. 310 317 Analysis of Electromagnetic Propulsion
More informationMODULE VII LARGE BODY WAVE DIFFRACTION
MODULE VII LARGE BODY WAVE DIFFRACTION 1.0 INTRODUCTION In the wave-structure interaction problems, it is classical to divide into two major classification: slender body interaction and large body interaction.
More informationAccuracy of the coherent potential approximation for a onedimensional array with a Gaussian distribution of fluctuations in the on-site potential
Accuracy of the coherent potential approximation for a onedimensional array with a Gaussian distribution of fluctuations in the on-site potential I. Avgin Department of Electrical and Electronics Engineering,
More information- particle with kinetic energy E strikes a barrier with height U 0 > E and width L. - classically the particle cannot overcome the barrier
Tunnel Effect: - particle with kinetic energy E strikes a barrier with height U 0 > E and width L - classically the particle cannot overcome the barrier - quantum mechanically the particle can penetrated
More informationChapter 22 The Hamiltonian and Lagrangian densities. from my book: Understanding Relativistic Quantum Field Theory. Hans de Vries
Chapter 22 The Hamiltonian and Lagrangian densities from my book: Understanding Relativistic Quantum Field Theory Hans de Vries January 2, 2009 2 Chapter Contents 22 The Hamiltonian and Lagrangian densities
More informationAcousto-optic modulator
1 of 3 Acousto-optic modulator F An acousto-optic modulator (AOM), also called a Bragg cell, uses the acousto-optic effect to diffract and shift the frequency of light using sound waves (usually at radio-frequency).
More informationF en = mω 0 2 x. We should regard this as a model of the response of an atom, rather than a classical model of the atom itself.
The Electron Oscillator/Lorentz Atom Consider a simple model of a classical atom, in which the electron is harmonically bound to the nucleus n x e F en = mω 0 2 x origin resonance frequency Note: We should
More informationSelf-Guided Intense Laser Pulse Propagation in Air
Nonlinear Analysis: Modelling and Control, 2000, v.6, No, 2-26 Self-Guided Intense Laser Pulse Propagation in Air R. Danielius, D. Mikalauskas, A. Dubietis and A. Piskarskas Department of Quantum Electronics,
More informationPHYSICAL QUANTITIES AND UNITS
1 PHYSICAL QUANTITIES AND UNITS Introduction Physics is the study of matter, its motion and the interaction between matter. Physics involves analysis of physical quantities, the interaction between them
More informationOptical nutation at a Raman-active transition
JETP LETTERS VOLUME 70, NUMBER 1 10 JULY 1999 Optical nutation at a Raman-active transition S. V. Anikeev, V. B. Morozov,* ) A. N. Olenin, and V. G. Tunkin M. V. Lomonosov Moscow State University, 119899
More informationUnderstanding Poles and Zeros
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.14 Analysis and Design of Feedback Control Systems Understanding Poles and Zeros 1 System Poles and Zeros The transfer function
More informationarxiv:physics/0004029v1 [physics.ed-ph] 14 Apr 2000
arxiv:physics/0004029v1 [physics.ed-ph] 14 Apr 2000 Lagrangians and Hamiltonians for High School Students John W. Norbury Physics Department and Center for Science Education, University of Wisconsin-Milwaukee,
More informationAcoustics of tachyon Fermi gas
Acoustics of tachyon Fermi gas arxiv:1103.2276v4 [hep-ph] 3 Jun 2011 Ernst Trojan and George V. Vlasov Moscow Institute of Physics and Technology PO Box 3, Moscow, 125080, Russia June 6, 2011 Abstract
More informationRotation: Moment of Inertia and Torque
Rotation: Moment of Inertia and Torque Every time we push a door open or tighten a bolt using a wrench, we apply a force that results in a rotational motion about a fixed axis. Through experience we learn
More informationUNIVERSITETET I OSLO
UNIVERSITETET I OSLO Det matematisk-naturvitenskapelige fakultet Exam in: FYS 310 Classical Mechanics and Electrodynamics Day of exam: Tuesday June 4, 013 Exam hours: 4 hours, beginning at 14:30 This examination
More informationMASTER OF SCIENCE IN PHYSICS MASTER OF SCIENCES IN PHYSICS (MS PHYS) (LIST OF COURSES BY SEMESTER, THESIS OPTION)
MASTER OF SCIENCE IN PHYSICS Admission Requirements 1. Possession of a BS degree from a reputable institution or, for non-physics majors, a GPA of 2.5 or better in at least 15 units in the following advanced
More informationCoherent control of a short and intensive XUV laser pulse in the spherical symmetric box potential
Coherent control of a short and intensive XUV laser pulse in the spherical symmetric box potential Imre Ferenc Barna and Péter Dombi 1 2 1) KFKI - AEKI Atomic Energy Research Institute of the Hungarian
More informationMonochromatic electromagnetic fields with maximum focal energy density
Moore et al. Vol. 4, No. 10 /October 007 /J. Opt. Soc. Am. A 3115 Monochromatic electromagnetic fields with maximum focal energy density Nicole J. Moore, 1, * Miguel A. Alonso, 1 and Colin J. R. Sheppard,3
More informationIntroduction to SME and Scattering Theory. Don Colladay. New College of Florida Sarasota, FL, 34243, U.S.A.
June 2012 Introduction to SME and Scattering Theory Don Colladay New College of Florida Sarasota, FL, 34243, U.S.A. This lecture was given at the IUCSS summer school during June of 2012. It contains a
More informationTorque Analyses of a Sliding Ladder
Torque Analyses of a Sliding Ladder 1 Problem Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (May 6, 2007) The problem of a ladder that slides without friction while
More informationChemistry 102 Summary June 24 th. Properties of Light
Chemistry 102 Summary June 24 th Properties of Light - Energy travels through space in the form of electromagnetic radiation (EMR). - Examples of types of EMR: radio waves, x-rays, microwaves, visible
More informationViscous flow through pipes of various cross-sections
IOP PUBLISHING Eur. J. Phys. 28 (2007 521 527 EUROPEAN JOURNAL OF PHYSICS doi:10.1088/0143-0807/28/3/014 Viscous flow through pipes of various cross-sections John Lekner School of Chemical and Physical
More informationGroup Theory and Chemistry
Group Theory and Chemistry Outline: Raman and infra-red spectroscopy Symmetry operations Point Groups and Schoenflies symbols Function space and matrix representation Reducible and irreducible representation
More informationwhere h = 6.62 10-34 J s
Electromagnetic Spectrum: Refer to Figure 12.1 Molecular Spectroscopy: Absorption of electromagnetic radiation: The absorptions and emissions of electromagnetic radiation are related molecular-level phenomena
More informationPerformance. 13. Climbing Flight
Performance 13. Climbing Flight In order to increase altitude, we must add energy to the aircraft. We can do this by increasing the thrust or power available. If we do that, one of three things can happen:
More informationInstability, dispersion management, and pattern formation in the superfluid flow of a BEC in a cylindrical waveguide
Instability, dispersion management, and pattern formation in the superfluid flow of a BEC in a cylindrical waveguide Michele Modugno LENS & Dipartimento di Fisica, Università di Firenze, Italy Workshop
More informationSound. References: L.D. Landau & E.M. Lifshitz: Fluid Mechanics, Chapter VIII F. Shu: The Physics of Astrophysics, Vol. 2, Gas Dynamics, Chapter 8
References: Sound L.D. Landau & E.M. Lifshitz: Fluid Mechanics, Chapter VIII F. Shu: The Physics of Astrophysics, Vol., Gas Dynamics, Chapter 8 1 Speed of sound The phenomenon of sound waves is one that
More informationAMPLIFICATION OF ATOMIC WAVES BY STIMULATED EMISSION OF ATOMS. Christian J. Borde
AMPLIFIATION OF ATOMI WAVES BY STIMULATED EMISSION OF ATOMS hristian J. Borde Laboratoire de Physique des Lasers, NRS/URA 8, Universite Paris-Nord, Villetaneuse, France. INTRODUTION: The recent development
More informationHigh Harmonic Generation from Multiple Orbitals in N 2
September 2008 SLAC-PUB-13406 High Harmonic Generation from Multiple Orbitals in N 2 Brian K. McFarland, Joseph P. Farrell, Philip H. Bucksbaum, Markus Gühr PULSE Institute, Stanford Linear Accelerator
More informationNonperturbative quantum dynamics
Nonperturbative quantum dynamics I. Laser interactions with atoms/molecules II. Model systems and TDDFT Manfred Lein, TDDFT school Benasque 24 p. Outline Laser interactions with atoms/molecules Classical
More informationarxiv:physics/9902008v1 [physics.class-ph] 2 Feb 1999
arxiv:physics/9902008v1 [physics.class-ph] 2 Feb 1999 The energy conservation law in classical electrodynamics E.G.Bessonov Abstract In the framework of the classical Maxwell-Lorentz electrodynamics the
More informationGRID AND PRISM SPECTROMETERS
FYSA230/2 GRID AND PRISM SPECTROMETERS 1. Introduction Electromagnetic radiation (e.g. visible light) experiences reflection, refraction, interference and diffraction phenomena when entering and passing
More informationChapter 18: The Structure of the Atom
Chapter 18: The Structure of the Atom 1. For most elements, an atom has A. no neutrons in the nucleus. B. more protons than electrons. C. less neutrons than electrons. D. just as many electrons as protons.
More informationHeating & Cooling in Molecular Clouds
Lecture 8: Cloud Stability Heating & Cooling in Molecular Clouds Balance of heating and cooling processes helps to set the temperature in the gas. This then sets the minimum internal pressure in a core
More informationThe Quantum Theory of the Emission and Absorption of Radiation.
P.A.M. Dirac, Proc. Roy. Soc., A114, 243 1927 The Quantum Theory of the Emission and Absorption of Radiation. P. A. M. Dirac, St. John s College, Cambridge, and Institute for Theoretical Physics, Copenhagen.
More informationOscillations. Vern Lindberg. June 10, 2010
Oscillations Vern Lindberg June 10, 2010 You have discussed oscillations in Vibs and Waves: we will therefore touch lightly on Chapter 3, mainly trying to refresh your memory and extend the concepts. 1
More information1 Lecture 3: Operators in Quantum Mechanics
1 Lecture 3: Operators in Quantum Mechanics 1.1 Basic notions of operator algebra. In the previous lectures we have met operators: ˆx and ˆp = i h they are called fundamental operators. Many operators
More informationPerpetual motion and driven dynamics of a mobile impurity in a quantum fluid
and driven dynamics of a mobile impurity in a quantum fluid Oleg Lychkovskiy Russian Quantum Center Seminaire du LPTMS, 01.12.2015 Seminaire du LPTMS, 01.12.2015 1 / Plan of the talk 1 Perpetual motion
More informationGeneral model of a structure-borne sound source and its application to shock vibration
General model of a structure-borne sound source and its application to shock vibration Y. Bobrovnitskii and T. Tomilina Mechanical Engineering Research Institute, 4, M. Kharitonievky Str., 101990 Moscow,
More informationThe Phenomenon of Photoelectric Emission:
The Photoelectric Effect. The Wave particle duality of light Light, like any other E.M.R (electromagnetic radiation) has got a dual nature. That is there are experiments that prove that it is made up of
More informationPHY4604 Introduction to Quantum Mechanics Fall 2004 Practice Test 3 November 22, 2004
PHY464 Introduction to Quantum Mechanics Fall 4 Practice Test 3 November, 4 These problems are similar but not identical to the actual test. One or two parts will actually show up.. Short answer. (a) Recall
More informationNONLINEAR ABSORPTION OF RUBY LASER LIGHT BY MOLECULAR POTASSIUM VAPOR
SOVIET PHYSICS JETP VOLUME 6, NUMBER 3 MARCH, 1968 NONLINEAR ABSORPTION OF RUBY LASER LIGHT BY MOLECULAR POTASSIUM VAPOR V. G. ABRAMOV, 0. V. KONSTANTINOV, N. N. KOSTIN, and V. A. KHODOVOI A. F. loffe
More informationCoherent control for the spherical symmetric box potential in short and intensive XUV laser fields
Cent. Eur. J. Phys. 6() 008 05-10 DOI: 10.478/s11534-008-0050-0 Central European Journal of Physics Coherent control for the spherical symmetric box potential in short and intensive XUV laser fields Research
More informationBlackbody radiation derivation of Planck s radiation low
Blackbody radiation derivation of Planck s radiation low 1 Classical theories of Lorentz and Debye: Lorentz (oscillator model): Electrons and ions of matter were treated as a simple harmonic oscillators
More information5. Scanning Near-Field Optical Microscopy 5.1. Resolution of conventional optical microscopy
5. Scanning Near-Field Optical Microscopy 5.1. Resolution of conventional optical microscopy Resolution of optical microscope is limited by diffraction. Light going through an aperture makes diffraction
More informationPHOTOELECTRIC EFFECT AND DUAL NATURE OF MATTER AND RADIATIONS
PHOTOELECTRIC EFFECT AND DUAL NATURE OF MATTER AND RADIATIONS 1. Photons 2. Photoelectric Effect 3. Experimental Set-up to study Photoelectric Effect 4. Effect of Intensity, Frequency, Potential on P.E.
More informationConcept 2. A. Description of light-matter interaction B. Quantitatities in spectroscopy
Concept 2 A. Description of light-matter interaction B. Quantitatities in spectroscopy Dipole approximation Rabi oscillations Einstein kinetics in two-level system B. Absorption: quantitative description
More informationNMR Techniques Applied to Mineral Oil, Water, and Ethanol
NMR Techniques Applied to Mineral Oil, Water, and Ethanol L. Bianchini and L. Coffey Physics Department, Brandeis University, MA, 02453 (Dated: February 24, 2010) Using a TeachSpin PS1-A pulsed NMR device,
More informationTime dependence in quantum mechanics Notes on Quantum Mechanics
Time dependence in quantum mechanics Notes on Quantum Mechanics http://quantum.bu.edu/notes/quantummechanics/timedependence.pdf Last updated Thursday, November 20, 2003 13:22:37-05:00 Copyright 2003 Dan
More informationComparison of approximations to the transition rate in the DDHMS preequilibrium model
EPJ Web of Conferences 69, 0 00 24 (204) DOI: 0.05/ epjconf/ 2046900024 C Owned by the authors, published by EDP Sciences, 204 Comparison of approximations to the transition rate in the DDHMS preequilibrium
More information1. Basics of LASER Physics
1. Basics of LASER Physics Dr. Sebastian Domsch (Dipl.-Phys.) Computer Assisted Clinical Medicine Medical Faculty Mannheim Heidelberg University Theodor-Kutzer-Ufer 1-3 D-68167 Mannheim, Germany sebastian.domsch@medma.uni-heidelberg.de
More information2.2 Magic with complex exponentials
2.2. MAGIC WITH COMPLEX EXPONENTIALS 97 2.2 Magic with complex exponentials We don t really know what aspects of complex variables you learned about in high school, so the goal here is to start more or
More informationA Guide to Acousto-Optic Modulators
A Guide to Acousto-Optic Modulators D. J. McCarron December 7, 2007 1 Introduction Acousto-optic modulators (AOMs) are useful devices which allow the frequency, intensity and direction of a laser beam
More informationy C-C i 2 3 1387 UCRL--96631 DE88 000963 Theory of Hultiphoton Ionization of Atoms by Strong, Short Pulsed lasers K. C. Kulander TAMP Group
y C-C i 2 3 1387 UCRL--96631 DE88 000963 UCRL-96631 frepkint Theory of Hultiphoton Ionization of Atoms by Strong, Short Pulsed lasers K. C. Kulander TAMP Group This paper was prepared for publication in
More informationWAVES AND FIELDS IN INHOMOGENEOUS MEDIA
WAVES AND FIELDS IN INHOMOGENEOUS MEDIA WENG CHO CHEW UNIVERSITY OF ILLINOIS URBANA-CHAMPAIGN IEEE PRESS Series on Electromagnetic Waves Donald G. Dudley, Series Editor IEEE Antennas and Propagation Society,
More informationExamples of Uniform EM Plane Waves
Examples of Uniform EM Plane Waves Outline Reminder of Wave Equation Reminder of Relation Between E & H Energy Transported by EM Waves (Poynting Vector) Examples of Energy Transport by EM Waves 1 Coupling
More informationRobust Algorithms for Current Deposition and Dynamic Load-balancing in a GPU Particle-in-Cell Code
Robust Algorithms for Current Deposition and Dynamic Load-balancing in a GPU Particle-in-Cell Code F. Rossi, S. Sinigardi, P. Londrillo & G. Turchetti University of Bologna & INFN GPU2014, Rome, Sept 17th
More informationTime Ordered Perturbation Theory
Michael Dine Department of Physics University of California, Santa Cruz October 2013 Quantization of the Free Electromagnetic Field We have so far quantized the free scalar field and the free Dirac field.
More informationTill now, almost all attention has been focussed on discussing the state of a quantum system.
Chapter 13 Observables and Measurements in Quantum Mechanics Till now, almost all attention has been focussed on discussing the state of a quantum system. As we have seen, this is most succinctly done
More informationWaves in a short cable at low frequencies, or just hand-waving?
Invited paper at the 23'rd International Conference on Noise and Fluctuations, 2015 Waves in a short cable at low frequencies, or just hand-waving? What does physics say? (Invited paper) L.B. Kish Department
More informationSpecial Theory of Relativity
June 1, 2010 1 1 J.D.Jackson, Classical Electrodynamics, 3rd Edition, Chapter 11 Introduction Einstein s theory of special relativity is based on the assumption (which might be a deep-rooted superstition
More informationIt has long been a goal to achieve higher spatial resolution in optical imaging and
Nano-optical Imaging using Scattering Scanning Near-field Optical Microscopy Fehmi Yasin, Advisor: Dr. Markus Raschke, Post-doc: Dr. Gregory Andreev, Graduate Student: Benjamin Pollard Department of Physics,
More informationarxiv:1201.6059v2 [physics.class-ph] 27 Aug 2012
Green s functions for Neumann boundary conditions Jerrold Franklin Department of Physics, Temple University, Philadelphia, PA 19122-682 arxiv:121.659v2 [physics.class-ph] 27 Aug 212 (Dated: August 28,
More informationNANOFLAM. Projet ANR Blanc 2011 BS0401001. Aide allouée: 337 000, durée 36+8 mois (fin : Mai 2015) Laboratoire H. Curien
Laboratoire H. Curien Centre de Physique Théorique F. Courvoisier R. Stoian & T. Itina A. Couairon NANOFLAM Projet ANR Blanc 2011 BS0401001 Contrôle de la filamentation et de la génération de plasma avec
More informationFeynman diagrams. 1 Aim of the game 2
Feynman diagrams Contents 1 Aim of the game 2 2 Rules 2 2.1 Vertices................................ 3 2.2 Anti-particles............................. 3 2.3 Distinct diagrams...........................
More informationMain properties of atoms and nucleus
Main properties of atoms and nucleus. Atom Structure.... Structure of Nuclei... 3. Definition of Isotopes... 4. Energy Characteristics of Nuclei... 5. Laws of Radioactive Nuclei Transformation... 3. Atom
More informationSection 6 Raman Scattering (lecture 10)
Section 6 Scattering (lecture 10) Previously: Quantum theory of atoms / molecules Quantum Mechanics Valence Atomic and Molecular Spectroscopy Scattering The scattering process Elastic (Rayleigh) and inelastic
More informationDoes Quantum Mechanics Make Sense? Size
Does Quantum Mechanics Make Sense? Some relatively simple concepts show why the answer is yes. Size Classical Mechanics Quantum Mechanics Relative Absolute What does relative vs. absolute size mean? Why
More informationPower Electronics. Prof. K. Gopakumar. Centre for Electronics Design and Technology. Indian Institute of Science, Bangalore.
Power Electronics Prof. K. Gopakumar Centre for Electronics Design and Technology Indian Institute of Science, Bangalore Lecture - 1 Electric Drive Today, we will start with the topic on industrial drive
More informationQuantum Computation with Bose-Einstein Condensation and. Capable of Solving NP-Complete and #P Problems. Abstract
Quantum Computation with Bose-Einstein Condensation and Capable of Solving NP-Complete and #P Problems Yu Shi Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom Abstract It
More informationTheory of electrons and positrons
P AUL A. M. DIRAC Theory of electrons and positrons Nobel Lecture, December 12, 1933 Matter has been found by experimental physicists to be made up of small particles of various kinds, the particles of
More informationCIVIL/CONSTRUCTION ENGINEERING TECHNOLOGY (CCET) TRANSFER ASSURANCE GUIDE (TAG) January 2, 2008
CIVIL/CONSTRUCTION ENGINEERING TECHNOLOGY (CCET) TRANSFER ASSURANCE GUIDE (TAG) January 2, 2008 Ohio Transfer Module: Ohio Transfer Module (OTM) Requirements: 36-40 semester hours / 54-60 quarter hours.
More informationScientific Programming
1 The wave equation Scientific Programming Wave Equation The wave equation describes how waves propagate: light waves, sound waves, oscillating strings, wave in a pond,... Suppose that the function h(x,t)
More information1 Variational calculation of a 1D bound state
TEORETISK FYSIK, KTH TENTAMEN I KVANTMEKANIK FÖRDJUPNINGSKURS EXAMINATION IN ADVANCED QUANTUM MECHAN- ICS Kvantmekanik fördjupningskurs SI38 för F4 Thursday December, 7, 8. 13. Write on each page: Name,
More informationPCV Project: Excitons in Molecular Spectroscopy
PCV Project: Excitons in Molecular Spectroscopy Introduction The concept of excitons was first introduced by Frenkel (1) in 1931 as a general excitation delocalization mechanism to account for the ability
More information= N 2 = 3π2 n = k 3 F. The kinetic energy of the uniform system is given by: 4πk 2 dk h2 k 2 2m. (2π) 3 0
Chapter 1 Thomas-Fermi Theory The Thomas-Fermi theory provides a functional form for the kinetic energy of a non-interacting electron gas in some known external potential V (r) (usually due to impurities)
More informationWave Function, ψ. Chapter 28 Atomic Physics. The Heisenberg Uncertainty Principle. Line Spectrum
Wave Function, ψ Chapter 28 Atomic Physics The Hydrogen Atom The Bohr Model Electron Waves in the Atom The value of Ψ 2 for a particular object at a certain place and time is proportional to the probability
More informationNear-field scanning optical microscopy (SNOM)
Adviser: dr. Maja Remškar Institut Jožef Stefan January 2010 1 2 3 4 5 6 Fluorescence Raman and surface enhanced Raman 7 Conventional optical microscopy-limited resolution Two broad classes of techniques
More informationReview of the isotope effect in the hydrogen spectrum
Review of the isotope effect in the hydrogen spectrum 1 Balmer and Rydberg Formulas By the middle of the 19th century it was well established that atoms emitted light at discrete wavelengths. This is in
More informationABSTRACT. We prove here that Newton s universal gravitation and. momentum conservation laws together reproduce Weinberg s relation.
The Speed of Light and the Hubble parameter: The Mass-Boom Effect Antonio Alfonso-Faus E.U.I.T. Aeronáutica Plaza Cardenal Cisneros s/n 8040 Madrid, Spain ABSTRACT. We prove here that Newton s universal
More informationPulsed Fourier Transform NMR The rotating frame of reference. The NMR Experiment. The Rotating Frame of Reference.
Pulsed Fourier Transform NR The rotating frame of reference The NR Eperiment. The Rotating Frame of Reference. When we perform a NR eperiment we disturb the equilibrium state of the sstem and then monitor
More informationNuclear Magnetic Resonance
Nuclear Magnetic Resonance Author: James Dragan Lab Partner: Stefan Evans Physics Department, Stony Brook University, Stony Brook, NY 794. (Dated: December 5, 23) We study the principles behind Nuclear
More information