# Book:Yoav Peleg/Quantum Mechanics

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## Yoav Peleg, Reuven Pnini and Elyahu Zaarur: Quantum Mechanics

Published $\text {1998}$, Schaum's Outlines

ISBN 0-07-054018-7.

### Contents

Chapter 1 INTRODUCTION
1.1 The Particle Nature of Electromagnetic Radiation. 1.2 The Duality of Light. 1.3 The Duality of Matter. 1.4 Wave-packets and the Uncertainty Relation.
Chapter 2 MATHEMATICAL BACKGROUND
2.1 The Complex Field $C$. 2.2 Vector Spaces over $C$. 2.3 Linear Operators and Matrices. 2.4 Eigenvectors and Eigenvalues. 2.5 Fourier Series and the Fourier Transform. 2.6 The Dirac Delta Function.
Chapter 3 THE SCHRODINGER EQUATION AND ITS APPLICATIONS
3.1 Wave Functions of a Single Particle. 3.2 The Schrödinger Equation. 3.3 Particle in a Time-independent Potential. 3.4 Scalar Product of Wave Functions; Operators. 3.5 Probability Density and Probability Current.
Chapter 4 THE FOUNDATIONS OF QUANTUM MECHANICS
4.1 Introduction. 4.2 Postulates in Quantum Mechanics. 4.3 Mean Value and Root-Mean-Square Deviation. 4.4 Commuting Observables. 4.5 Function of an Operator. 4.6 Hermitian Conjugation. 4.7 Discrete and Continuous State Spaces. 4.8 Representations. 4.9 The Time Evolution. 4.10 Uncertainty Relations. 4.11 The Schrödinger and Heisenberg Pictures.
Chapter 5 HARMONIC OSCILLATOR
5.1 Introduction. 5.2 The Hermite Polynomials. 5.3 Two- and Three-Dimensional Harmonic Oscillators. 5.4 Operator Methods for a Harmonic Oscillator.
Chapter 6 ANGULAR MOMENTUM
6.1 Introduction. 6.2 Commutation Relations. 6.3 Lowering and Raising Operators. 6.4 Algebra of Angular Momentum. 6.5 Differential Representations. 6.6 Matrix Representation of an Angular Momentum. 6.7 Spherical Symmetry Potentials. 6.8 Angular Momentum and Rotations.
Chapter 7 SPIN
7.1 Definitions. 7.2 Spin 1/2. 7.3 Pauli Matrices. 7.4 Lowering and Raising Operators. 7.5 Rotations in the Spin Space. 7.6 Interaction with a Magnetic Field.
Chapter 8 HYDROGEN-LIKE ATOMS
8.1 A Particle in a Central Potential. 8.2 Two Interacting Particles. 8.3 The Hydrogen Atom. 8.4 Energy Levels of the Hydrogen Atom. 8.5 Mean Value Expressions. 8.6 Hydrogen-like Atoms.
Chapter 9 PARTICLE MOTION IN AN ELECTROMAGNETIC FIELD
9.1 The Electromagnetic Field and Its Associated Potentials. 9.2 The Hamiltonian of a Particle in the Electromagnetic Field. 9.3 Probability Density and Probability Current. 9.4 The Magnetic Moment. 9.5 Units.
Chapter 10 SOLUTION METHODS IN QUANTUM MECHANICS - PART A
10.1 Time-Independent Perturbation Theory. 10.2 Perturbation of a Nondegenerate Level. 10.3 Perturbation of a Degenerate State. 10.4 Time-Dependent Perturbation Theory.
Chapter 11 SOLUTION METHODS IN QUANTUM MECHANICS - PART B
11.1 The Variational Method. 11.2 Semiclassical Approximation (The WKB Approximation).
Chapter 12 NUMERICAL METHODS IN QUANTUM MECHANICS
12.1 Numerical Quadrature. 12.2 Roots. 12.3 Integration of Ordinary Differential Equations.
Chaper 13 IDENTICAL PARTICLES
13.1 Introduction. 13.2 Permutations and Symmetries of Wave Functions. 13.3 Bosons and Fermions.
Chapter 14 ADDITION OF ANGULAR MOMENTA
14.1 Introduction. 14.2 $\left\{{\mathbf j_1^2, \mathbf j_2^2, \mathbf J^2, \mathbf J_z}\right\}$ Basis. 14.3 Clebsch-Gordan Coefficients.
Chapter 15 SCATTERING THEORY
15.1 Cross Section. 15.2 Stationary Scattering States. 15.3 Born Approximation. 15.4 Partial Wave Expansions. 15.5 Scattering of Identical Particles.
Chapter 16 SEMICLASSICAL TREATMENT OF RADIATION
16.1 The Interaction of Radiation with Atomic Systems. 16.2 Time-Dependent Perturbation Theory. 16.3 Transition Rate. 16.4 Multipole Transitions. 16.5 Spontaneous Emission.
Appendix MATHEMATICAL APPENDIX
A.1 Fourier Series and Fourier Transform. A.2 The Dirac $\delta$-function. A.3 Hermite Polynomials. A.4 Legendre Polynomials. A.5 Associated Legendre Functions. A.6 Spherical Harmonics. A.7 Associated Laguerre Polynomials. A.8 Spherical Bessel Functions.
INDEX

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## Source work progress

Bogged down in exactly what the product of linear operators means.
Analysis starts at chapter $2$. Chapter $1$ still to be addressed.