How to Be a Quantum Mechanic is an introduction to quantum mechanics at the upper-division level. It begins with wave-particle duality and ends with a brief introduction to the Dirac equation. Two attitudes went into its writing: Examples are the best way to get into a subject, and numbers and equations alone do not always sum to understanding. The author taught for 40 years at the University of California, Berkeley. He earned his Ph.D. at Berkeley, in experimental elementary-particle physics in the group led by Luis Alvarez.
Author(s): Charles G. Wohl
Publisher: CRC Press
Year: 2022
Language: English
Pages: 394
City: Boca Raton
Cover
Half Title
Title Page
Copyright Page
Dedication
CONTENTS
1. Strangest Things
1.1. Planck, Einstein, Compton, de Broglie
1.2. Neutron Interference
1.3. Photon Interference
1.4. Bohr and Hydrogen
Problems
2. The Schrodinger Equation. Bound States
2.1. The Time-Dependent Schrodinger Equation
2.2. The Wave Function
2.3. The Time-Independent Equation. Energy Eigenstates
2.4. The Infinite Square Well
2.5. The Finite Square Well
2.6. The Delta-Function Well
2.7. Schrodinger in Three Dimensions
2.8. Two Important Energy Eigenstates
2.9. Qualitative Properties of Bound Energy Eigenstates
Problems
3. Simple Approximations for Bound States
3.1. Dimensions and Scaling
3.2. Fitting Wavelengths in a Well
3.3. Guessing the Ground-State Wave Function
3.4. Useful Integrals
Problems
4. Scattering in One Dimension
4.1. Particle Densities and Currents
4.2. Scattering by a Step
4.3. A General Rectangular Barrier
4.4. A Simple Rectangular Barrier
4.5. Designing with Rectangular Barriers
4.6. Thin Films and Light
4.7. Weak Tunneling
Problems
5. Mathematical Formalism
5.1. Vector Spaces. Dirac Notation
5.2. States as Vectors
5.3. Operators
5.4. Successive Operations. Commutators
5.5. Operators as Matrices
5.6. Expectation Values
5.7. More Theorems
5.8. Revised Rules
Problems
6. The Harmonic Oscillator
6.1. The Classical Oscillator
6.2. The Quantum Oscillator: Series Solution
6.3. The Operator Solution
6.4. States as Vectors, Operators as Matrices
Problems
7. Uncertainty Relations. Simultaneous Eigenstates
7.1. Heisenberg Uncertainty Relations
7.2. The Schwarz Inequality
7.3. Proof of Uncertainty Relations
7.4. Fourier Transforms. Momentum Space
7.5. Time and Energy
7.6. When Operators Commute
Problems
8. Angular Momentum
8.1. Central Forces. Separation of Variables
8.2. Angular Momentum Commutation Relations
8.3. The Operator Solution
8.4. Certainty and Uncertainty
8.5. States as Vectors, Operators as Matrices (Again)
8.6. Differential Operators for Orbital Angular Momentum
8.7. Spherical Harmonics
8.8. Angular Momentum and the Oscillator
Problems
9. Hydrogen. The Isotropic Oscillator
9.1. The Effective Potential Energy
9.2. The Hydrogen Bound-State Energies
9.3. The Hydrogen Eigenfunctions
9.4. The Isotropic-Oscillator Energies
9.5. The Oscillator Eigenfunctions
9.6. Hydrogen and the Oscillator
Problems
10. Spin-1/2 Particles
10.1. Spinors. Eigenvalues and Eigenstates
10.2. The Polarization Vector
10.3. Magnetic Interactions and Zeeman Splitting
10.4. Time Dependence and Larmor Precession
10.5. Time Dependence and Magnetic Resonance
10.6. Stern-Gerlach Experiments
10.7. Polarization and Light
Problems
11. Hyperfine Splitting. Two Angular Momenta. Isospin
11.1. Hyperfine Structure of the Hydrogen Ground State
11.2. The 21-cm Line and Astronomy
11.3. Coupling Two Spin-1/2 Particles
11.4. Coupling Any Two Angular Momenta
11.5. Clebsch-Gordan Coefficients
11.6. Particle Multiplets and Isospin
Problems
12. Cryptography. The EPR Argument. Bell’s Inequality
12.1. Quantum Cryptography
12.2. The EPR Argument
12.3. Bell’s Inequality
Problems
13. Time-Independent Perturbation Theory
13.1. The Nondegenerate Recipes
13.2. Examples of Nondegenerate Theory
13.3. The Nondegenerate Derivations
13.4. The Degenerate Recipe
13.5. Two Selection Rules. A Useful Relation
13.6. The Stark Effect in Hydrogen (Strong-Field Case)
13.7. Hydrogen Fine Structure: Experiment
13.8. Hydrogen Fine Structure: Theory
13.9. Atomic Magnetic Moments
13.10. The Zeeman Effect in Hydrogen (Weak-Field Case)
Problems
14. Identical Particles
14.1. Electrons in a Box
14.2. Electrons in an Atom: the Periodic Table
14.3. Electrons in an Atom: More Pauli
14.4. Two-Electron Symmetries
14.5. The Helium Ground State
14.6. The Electron-Electron Repulsion Integral
14.7. Helium Excited States. Exchange Degeneracy
14.8. Fermions and Bosons. How to Count. Symmetries
Problems
15. Time-Dependent Perturbations. Planck and Einstein
15.1. Sudden Changes
15.2. Time-Dependent Perturbation Theory
15.3. Magnetic Resonance (Again)
15.4. Hydrogen in an Electromagnetic Wave
15.5. Averaging over Polarizations and Frequencies
15.6. The Boltzmann Factor
15.7. Planck’s Oscillators
15.8. Black-Body Radiation
15.9. Einstein’s A and B Coefficients
15.10. Decay Lifetimes
Problems
16. Scattering
16.1. Solid Angle
16.2. Classical Particle Scattering. Rutherford
16.3. The Scattering Amplitude
16.4. The Born Approximation
16.5. Kinematics
16.6. Partial-Wave Theory
16.7. Partial-Wave Examples
16.8. Scattering of Identical Particles
Problems
17. The Dirac Equation
17.1. Dirac at Play
17.2. Spin!
Problems
Sources of Quotes
Index
