Schaum's Quantum Mechanics (2nd Edition) by Eugene Hecht, Yoav Peleg, Reuven Pnini, Elyahu Zaarur
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Schaum's Quantum Mechanics (2nd Edition) written by
Eugene Hecht , Ph.D., written Schaum’s Outline of Optics and Schaum’s Outline of College Physics
Yoav Peleg , Ph.D., researcher with Motorola, Israel
Reuven Pnini , Ph.D., Chief Scientifi c Editor of Rakefet Publishing Ltd. and
Elyahu Zaarur , M.Sc., Managing Director of Rakefet Publishing Ltd.
The main purpose of this second edition of Quantum Mechanics is to make an already fine book more usable for the student reader. Accordingly, a great deal of effort has been given to simplifying and standardizing the notation. For example, a number of modern QM textbooks now distinguish operators from other quantities by placing a cap (^) over the corresponding symbol for the operator. This simple emendation can nonetheless be very helpful to the student and that practice has been adopted throughout this edition. Similarly I have avoided using the same symbol to represent different quantities, inasmuch as this can be unduly confusing. Wherever necessary, discussions have been extended and the prose has been clarified. The allbut unavoidable typographical and other minor first-edition errors have been corrected. Additionally, all of the art has been redrawn to improve visual readability, content, clarity, and accuracy. A substantial number of new introductory-level solved problems have been added to ensure that the student can gain a good grasp of the basics before approaching a more challenging range of questions. Indeed, it is my intention to add more such problems in future editions.
Schaum's Quantum Mechanics (2nd Edition) written by
Eugene Hecht, Yoav Peleg, Reuven Pnini, Elyahu Zaarur
cover the following topics.
1. Introduction
1.1 The Particle Nature of Electromagnetic Radiation
1.2 Quantum Particles
1.3 Wave Packets and the Uncertainty Relation
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
3. The Schrödinger Equation and Its Applications
3.1 Wavefunctions of a Single Particle
3.2 The Schrödinger Equation
3.3 Particle in a Time-Independent Potential
3.4 Scalar Product of Wavefunctions: Operators
3.5 Probability Density and Probability Current
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
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
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
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
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
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
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
11. Solution Methods in Quantum Mechanics—Part B
11.1 The Variational Method
11.2 Semiclassical Approximation (The WKB Approximation)
12. Numerical Methods in Quantum Mechanics
12.1 Numerical Quadrature
12.2 Roots
12.3 Integration of Ordinary Differential Equations
13. Identical Particles
13.1 Introduction
13.2 Permutations and Symmetries of Wavefunctions
13.3 Bosons and Fermions
14. Addition of Angular Momenta
14.1 Introduction
14.2 {Jˆ , Jˆ , Jˆ , Jˆ } 1222 2z Basis
14.3 Clebsch–Gordan Coefficients
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
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
Mathematical Appendix
A.1 Fourier Series and Fourier Transform
A.2 The Dirac d-Function
A.3 Hermite Polynomials
A.4 Legendre Polynomials
A.5 Associated Legendre Functions
A.6 Spherical Harmonics
A.7 Associated Laguerre
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