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quantum - The University of Queensland Department of...

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Unformatted text preview: The University of Queensland Department of Physics 2004 Lecture notes of the undergraduate course PHYS2041 QUANTUM PHYSICS Lecturer: Dr. Zbigniew Ficek Physics Annexe(6): Rm. 436 Ph: 3365 2331 email: [email protected] Contact Hours: 1. Tuesday: 11am , Rm. 7-302 (Lectures) 2. Friday: 11am , Rm. 7-302 (Tutorials) Consultation Hours: Wednesday , 2pm- 4pm Contents General Bibliography 5 Assumed Background 6 Introduction 9 1 Radiation (Light) is a Wave 10 1.1 Wave equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2 Energy of the EM wave . . . . . . . . . . . . . . . . . . . . . . 12 2 Difficulties of the Wave Theory of Radiation 17 2.1 Discovery of the electron . . . . . . . . . . . . . . . . . . . . . 17 2.2 Discovery of X-rays . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Photoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4 Compton scattering . . . . . . . . . . . . . . . . . . . . . . . . 22 2.5 Discrete atomic spectra . . . . . . . . . . . . . . . . . . . . . . 23 3 Black-Body Radiation 25 3.1 Number of radiation modes . . . . . . . . . . . . . . . . . . . 25 3.2 Equipartition theorem . . . . . . . . . . . . . . . . . . . . . . 28 4 Planck’s Quantum Hypothesis 31 4.1 Boltzmann distribution function . . . . . . . . . . . . . . . . . 31 4.2 Planck’s formula for I ( λ ) . . . . . . . . . . . . . . . . . . . . . 32 4.3 Photoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . 37 4.4 Compton scattering . . . . . . . . . . . . . . . . . . . . . . . . 37 5 The Bohr Model 41 5.1 The hydrogen atom . . . . . . . . . . . . . . . . . . . . . . . . 41 5.2 X-rays characteristic spectra . . . . . . . . . . . . . . . . . . . 44 5.3 Difficulties of the Bohr model . . . . . . . . . . . . . . . . . . 45 6 Duality of Light and Matter 47 6.1 Matter waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 6.2 Matter wave interpretation of the Bohr’s model . . . . . . . . 50 6.3 Wave function . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2 6.4 Physical meaning of the wave function . . . . . . . . . . . . . 53 6.5 Phase and group velocities . . . . . . . . . . . . . . . . . . . . 55 6.6 The Heisenberg uncertainty principle . . . . . . . . . . . . . . 59 6.7 The superposition principle . . . . . . . . . . . . . . . . . . . 61 6.8 Wave packets . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 7 Schr¨ odinger Equation 66 7.1 Schr¨ odinger equation of a free particle . . . . . . . . . . . . . 66 7.2 Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 7.3 Schr¨ odinger equation of a particle in an external potential . . 70 7.4 Equation of continuity . . . . . . . . . . . . . . . . . . . . . . 73 8 Applications of the Schr¨ odinger Equation: Potential (Quan- tum) Wells 79 8.1 Infinite potential quantum well . . . . . . . . . . . . . . . . . 81 8.2 Finite square-well potential . . . . . . . . . . . . . . . . . . . 88 8.3 Quantum tunneling . . . . . . . . . . . . . . . . . . . . . . . .Quantum tunneling ....
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