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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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