Nanoelectronics. Chapter 2 Classical Particles, Classical Waves, and Quantum Particles.

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1 Nanoelectronics Chapter 2 Classical Particles, Classical Waves, and Quantum Particles 1

2 Electron Double-Slit Experiment 2

3 2.1 Comparison of Classical and Quantum Systems Classical physics is to describe the exact state of a particle, how fast it will travel at a certain instant of time. Quantum mechanics: it is impossible to measure precisely both the position and momentum of a particle, theoretically impossible. Quantum theory is truly a probabilistic theory. 3

4 2.2 Origins of Quantum Mechanics Photoelectric effect: if light is incident on a metal, some energy carried by the light can be transferred to electrons at the metal s surface, and the electrons gain enough energy to escape from the metal. Kinetic energy of photo-emitted electrons does not increase as the intensity of light increases. When the frequency of light increases, more energetic electrons were emitted. 4

5 2.3 Light as a Wave, Light as a Particle Light as a particle or perhaps a wave the early years A little later Light as a wave Interference Ψ = Ψ + Ψ = + ( ) = (1 + ) If kl = 0, 2π, 4π, Ψ = 2 If kl = π, 3π, 5π, Ψ =0 Young s Experiment What to expect from Waves 5

6 Young s Experiment Ψ r j is the distance from jth slit to observation location on the screen 6

7 Finally, Light as a Quantum Particle Young s Experiment one slit at a time = ( ) Young s Experiment What to expect with classical particles = + 7

8 Finally, Light as a Quantum Particle Young s Experiment and the Concept of Photons one more time with light, but slowly. If the intensity is reduced enough, we would find that energy is not arriving continuously, but in discrete bursts, pointing to a particle-like nature of light. Photon: = = ħ 8

9 Finally, Light as a Quantum Particle Young s Experiment A very strange result concerning interference Light exhibits bot wave-like and particle-like behavior, is clearly neither a classical wave not a classical particle. We call this a quantum particle. 9

10 2.4 Electrons as Particles, Electrons as Waves Electrons as Particles - The Early Years It was found in late 1800s by J.J. Thomson Electrons (and everything else) as Quantum Particles Louis de Broglie in 1923 suggested that all particles having energy E and momentum p should have wavelike properties, too. = ; = ħ ; k is wavenumber, - matter waves, for 1Kg object: =

11 Electrons as Waves The wavelength of a 1 ev photon: = = 1.24 The wavelength of a 1 ev electron: h = = Why we cannot see individual photon or the granularity of light flow? 1 uw light has photon/s 11

12 2.4.3 Further Development of Quantum Mechanics Schrodinger s equation (In double-slit experiment) the wave of each photon interferes with itself in passing through the two slits. Or the photon pass both slits at the same time Heisenberg uncertainty principle Δ Δ ħ/2 Particles with integral spin: bosons, Particles with half-integral spin: fermions Pauli exclusion principle: two or more identical fermions cannot occupy the same quantum state. 12

13 2.5 Wavepackets and Uncertainty For a particle with mass m: = ħ = ħ Dispersion relations: ( ) = ħ Phase velocity: = It seems reasonable to model a quantum particle as being associated with a wavepacket, since a wavepacket exhibits wave-like behavior, viewed like a particles from a far distance. Δ Δ = /2 13

14 2.5 Wavepackets and Uncertainty Δ Δ = /2 A wavepacket tightly confined in space Is made up of plane waves having a large Spread in wavenumbers, vise versa. Group velocity: = Wavepacket can change shape = 2 14

15 2.6 Main Points Classical particles Quantum particle s position and momentum Electron s wavelength Idea of spin and Pauli exclusion principle Fermions and bosons Wavepacket concepts: phase velocity and group velocity 15

16 2.7 Problems 2, 3, 4, 11, 12 16

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