course book quantum - Quantum Mechanics Richard Fitzpatrick...

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Unformatted text preview: Quantum Mechanics Richard Fitzpatrick Professor of Physics The University of Texas at Austin Contents 1 Introduction 7 1.1 Intended audience . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Major Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Aim of Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Outline of Course . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 I Fundamentals 10 2 Probability Theory 11 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 What is Probability? . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Combining Probabilities . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 The Mean, Variance, and Standard Deviation . . . . . . . . . . . . 14 2.5 Continuous Probability Distributions . . . . . . . . . . . . . . . . . 16 3 Wave-Particle Duality 18 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2 Classical Light-Waves . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3 The Photoelectric Effect . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4 Quantum Theory of Light . . . . . . . . . . . . . . . . . . . . . . . 22 3.5 Classical Interference of Light-Waves . . . . . . . . . . . . . . . . . 23 3.6 Quantum Interference of Light . . . . . . . . . . . . . . . . . . . . 25 3.7 Classical Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.8 Quantum Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.9 Wave-Packets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.10 Evolution of Wave-Packets . . . . . . . . . . . . . . . . . . . . . . . 33 3.11 Heisenbergs Uncertainty Principle . . . . . . . . . . . . . . . . . . 36 3.12 Schrodingers Equation . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.13 Collapse of the Wave-Function . . . . . . . . . . . . . . . . . . . . 41 4 Fundamentals of Quantum Mechanics 44 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2 Schrodingers Equation . . . . . . . . . . . . . . . . . . . . . . . . . 44 2 4.3 Normalization of the Wave-Function . . . . . . . . . . . . . . . . . 44 4.4 Expectation Values and Variances . . . . . . . . . . . . . . . . . . . 47 4.5 Ehrenfests Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.6 Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.7 The Momentum Representation . . . . . . . . . . . . . . . . . . . . 54 4.8 The Uncertainty Principle . . . . . . . . . . . . . . . . . . . . . . . 58 4.9 Eigenstates and Eigenvalues . . . . . . . . . . . . . . . . . . . . . . 61 4.10 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.11 Continuous Eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . 67 4.12 Stationary States . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5 One-Dimensional Potentials 73 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73....
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This note was uploaded on 03/29/2010 for the course PHYS 3318 taught by Professor Flanagan during the Spring '08 term at Cornell University (Engineering School).

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course book quantum - Quantum Mechanics Richard Fitzpatrick...

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