The author has published two texts on classical physics, Introduction to Classical Mechanics and Introduction to Electricity and Magnetism, both meant for initial one-quarter physics courses. The latter is based on a course taught at Stanford several years ago with over 400 students enrolled. These lectures, aimed at the very best students, assume a good concurrent course in calculus; they are otherwise self-contained. Both texts contain an extensive set of accessible problems that enhances and extends the coverage. As an aid to teaching and learning, the solutions to these problems have now been published in additional texts. The present text completes the first-year introduction to physics with a set of lectures on Introduction to Quantum Mechanics, the very successful theory of the microscopic world. The Schrödinger equation is motivated and presented. Several applications are explored, including scattering and transition rates. The applications are extended to include quantum electrodynamics and quantum statistics. There is a discussion of quantum measurements. The lectures then arrive at a formal presentation of quantum theory together with a summary of its postulates. A concluding chapter provides a brief introduction to relativistic quantum mechanics. An extensive set of accessible problems again enhances and extends the coverage. The goal of these three texts is to provide students and teachers alike with a good, understandable, introduction to the fundamentals of classical and quantum physics.
Author(s): John Dirk Walecka
Edition: 1
Publisher: WSPC
Year: 2021
Language: English
Pages: 160
Tags: quantum, mechanics
Contents
Preface
1. Motivation
1.1 Classical Optics
1.2 Planck Distribution
1.3 Photons
1.4 Davisson–Germer Experiment
2. Wave Packet for Free Particle
2.1 de Broglie Relation
2.2 Schrödinger Equation
2.3 Interpretation
2.4 Stationary States
2.5 Eigenfunctions and Eigenvalues
2.6 General Solution
3. Include Potential V(x)
3.1 Schrödinger Equation
3.2 Particle in a Box
3.3 Boundary Conditions
3.4 Barrier Penetration
3.5 Bound States
3.6 Higher Dimensions
3.7 Perturbation Theory
3.7.1 Non-Degenerate Perturbation Theory
4. Scattering
4.1 Incident Plane Wave
4.2 S-Wave Scattering
4.3 Spherical Square Well
4.4 Scattering Boundary Condition
4.5 Cross-Section
4.6 High Energy
5. Transition Rate
5.1 Model Problem
5.2 Golden Rule
5.3 Density of Final States
5.4 Incident Flux
5.5 Summary
5.6 Born Approximation
5.7 Two-State Mixing
6. Quantum Electrodynamics
6.1 Hamiltonian
6.2 Schrödinger Equation
6.3 Ionization in Oscillating Electric Field
6.4 Interaction With the Radiation Field
6.5 Photoionization
6.6 Normal Mode Expansion of the Electromagnetic Field
6.7 Quantization of the Oscillator
6.8 Quantization of the Electromagnetic Field
6.9 Radiative Decay
6.10 Schrödinger Picture
6.11 Lasers
7. Quantum Statistics
7.1 Bosons
7.1.1 Bose Condensation
7.2 Fermions
7.3 Connection Between Spin and Statistics
8. Quantum Measurements
8.1 Stern–Gerlach Experiment
8.2 Reduction of the Basis
8.3 A Second Experiment — π0 Decay
9. Formal Structure of Quantum Mechanics
9.1 Hilbert Space
9.2 Component Form
9.3 The Schrödinger Equation
9.4 Hermitian Operators
9.5 Commutation Relations
9.6 Ehrenfest’s Theorem
9.7 Other Pictures
10. Quantum Mechanics Postulates
11. Relativity
11.1 Special Relativity
11.2 Massive Scalar Field
11.3 The Dirac Equation
11.3.1 Non-Relativistic Reduction
11.3.2 Dirac Hole Theory
11.3.3 Electromagnetic Interactions
11.4 Path Integrals
12. Problems
Appendix A Electromagnetic Field in Normal Modes
Appendix B Significant Names in Quantum Mechanics—Theory and Applications
Bibliography
Index
