THE HISTORY OF QUANTUM MECHANICS

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1 THE HISTORY OF QUANTUM MECHANICS Solvay Conference 197 If quantum mechanics hasn't profoundly shocked you, you haven't understood it yet Niels Bohr

2 The more success quantum theory has, the sillier it looks. Albert Einstein Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing...in any case, I am convinced that He doesn't play dice. Albert Einstein

3 Nobody understands quantum theory. Richard Feynman The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. Paul A. M. Dirac

4 I do not like quantum mechanics, and I am sorry I ever had anything to do with it. Erwin Schrödinger Classical mechanics Planetary orbits Around 1610: Johannes Kepler formulated the laws of planetary orbits.

5 Classical mechanics 1687 Isaac Newton Philosophiae Naturalis Principia Mathematica Newton s laws of motion Lagrange, Laplace Hamilton Mathematical toolkit Deterministic worldview x(0) =..., v(0) =... x( t) =..., v( t) =... Light 1690 Newton 1801: Young: Interference wave nature of light 1873: James Clerk Maxwell s theory of electromagnetism

6 Lord Kelvin, around 1880 "There is nothing new to be discovered in physics now, All that remains is more and more precise measurement." Problems around Black-body radiation UV-catastrophe. Photoelectric effect 3. The linespectrum of atoms

7 1. Black-body radiation, UV-catastrophe Classical physics: Rayleigh-Jeans formula 1900: Max Planck Only a quantized amount of energy can be absorbed or emitted. E = n hν (Nobelprize 1918) Planck s formula for blackbody radiation Reproduce measurements. Photoelectric effect 1887 Experimental measurements by Hertz & Hallwachs: Negative charges are released upon radiation of UV light. 1895: Thomson discovers electron 1899: Lenard: photo-electrons E kin independent of I. E kin depends on the frequency of the light A. Einstein: The energy of the light is quantized (Nobelprize 191) h ν W + = 0 E kin 1916 The model by Einstein was confirmed experimentally by R. A. Millikan. The constant h was determined. (Nobelprize 193)

8 3. The line-spectrum of atoms 1903: J. J. Thomson s atom model H. Nagaoka s atom model (Nobel prize 1906) Plum-pudding model Problem: Classical physics Electrons should emit radiation when circulating in the orbit. 1910: A. E. Haas: Theoretical model for the Thomson model including h. h had before only been included in optics. Saturnian atomic model The model was vividly discussed at the Solvay conference in The line-spectrum of atoms 1911: Ernest Rutherford s scattering of α particles towards Au-foil Atomic nuclei 180: Spectrum of sunlight: 4 dark lines Fraunhofer lines ~1870 Atomic spectra (Rutherford, Cambridge) Hα, Hβ Hγ Hδ Balmer lines

9 3. Atomernas linjespektrum Adolf Erik Nordenskiöld (Arctic explorations) Was trying to understand the spectrum of the H-atom. 1887: Johannes Rydberg 1 λ 1 1 R n i n f = QUANTUM MECHANICS STARTS TO EVOLVE

10 The Bohr model In 1913 Niels Bohr developed the Bohr model of the hydrogen atom, which could explain the observed spectrum. (Nobel prize 19) L = mvr = nh E n E =, n n 1 = 1,,3,... Why are these orbitals stable? Problem to describe other atoms than H. De Broglie wave length 194 Louis debroglie (PhD thesis) (Nobel prize 199) If light can have particle properties, then particles can have wave properties. λ = h p Einstein approved the PhD thesis! ~190 Ramsauer-Townsend effect: elastic scattering of electrons towards a noble gas. Oscillation in the cross section that cannot be explained classically. 196: Davisson-Germer: electron diffraction towards Ni-crystal. Bragg-diffraktion (Nobelprize 1937)

11 Heisenberg s matrix algebra Werner Heisenberg tried to understand the line spectrum of H-atom. - Especially the Zeeman effect (what happens with the spectrum when the atom is placed in a magnetic field). (Worked with Bohn in Copenhagen and then at Göttingen, Germany) 195 Develops a new matrix algebra during 6 months (Nobelprize193) Heisenberg s matrix algebra 195 Max Born (Göttingen) formulates a new quantum mechanics with the matrix theory. Was published two months after the article of Heisenberg. Commutators AB BA Conservation of energy, momentum and angular momentum. Bohr s energy levels Maxwell s electromagnetic theory

12 Schrödinger equation Erwin Schrödinger, Austrian (tuberculosis) Quantisierung als Eigenwertproblem Annalen der Physik, 196 Combined the classical wave equation with the debroglie wave length. (Nobelprize 1933) Article I:Time-independent Schrödinger equation for the H-atom. Schrödinger equation Hamilton-Jacobi eq. for timeindependent systems (analytical mechanics)

13 Schrödinger equation Radial SE for H-atom n=l! Schrödinger equation Quantization of energy levels l=n To obtain the Bohr s formula K=ħ!

14 Schrödinger equation Quantisierung als Eigenwertproblem Annalen der Physik, 196 Article I:Time-independent Schrödinger equation h m d dx + V ( x) ψ ( x) = Eψ ( x) Article IV: Time-dependent Schrödinger equation ih Ψ t h d x, t) = m dx ( + V ( x, t) Ψ( x, t) (Nobelprize 1933) Schrödinger equation 196: Heisenberg s matrixtheory and the Schrödinger equation were found to be mathematical equivalent. (Seminar in Munich with Sommerfeld). 196: Max Born s statistical interpretation Copenhagen interpretation b a Ψ( x, t) probability to find the particle dx = within a x b at time t Wave function Ψ = i cψ i i measurement result ψ i Probability to obtain a given result = c i Born s statistical interpretation God plays dice Collapse of the wave function. Bohr, Heisenberg, Pauli

15 Uncertainty principle 197: Heisenberg formulated the uncertainty principle [ x, pˆ x ] = ih σ x σ y h Quantum mechanics relativity 198: Paul A.M Dirac: Combined quantum mechnics with special relativity. (Nobelprize 1933) Dirac equation βmc + k= 1 Antimatter α k pkc ψ ( x, t) = ih 3 ψ ( x, t) t

16 Schrödinger s cat 1935: E. Schrödinger and A. Einstein proposed the gedanke experiment of the Schrödinger s cat. Problem with the Copenhagen interpretation Ψcat = c1ψdead + c Ψ alive Many Wolds interpretation 1957 Hugh Everett: Alternative interpretation to the Copenhagen interpretation

17 QUANTUM MECHANICS OF TODAY Bose-Einstein Condensate Cornell & Wiemann showed in 1995 that when a gas of bosons (87Rb) cool down towards absolute zero, the debroglie wavelengths of the atoms will start to overlap and a condensate is formed. (Nobelprize 001) All bosons occupy the lowest quantum level. Quantum mechanics at a macroscopic level.

18 Quantum computers Superposition principle Qubits 100> result> Gate TDSE Quantum computers Superposition principle Interaction with the environment -decoherence Qubits c1 000>+c 100>+c3 010> + Gate TDSE result>

19 Science Sept Study of the electronic wavefunction of Hexabenzocorane molecule using Atomic Force microscopy. High temperature superconductivity Some unsolved problems Bednorz & Müller 1986: Perovskite material can be superconductive at temperatures above the boiling point of liquid (77 K). (Nobelprize 1987) Must be described quantum mechanically, but no theory is developed. Quantum gravity How can gravity be described quantum mechanically? Combine quantum mechanics with general relativity.