Quantum Theory

Quantum Theory

Elements

1st Edition - January 1, 1961

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  • Editor: D. R. Bates
  • eBook ISBN: 9781483275888

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Description

Quantum Theory: A Treatise in Three Volumes, I: Elements focuses on the principles, methodologies, and approaches involved in quantum theory, including quantum mechanics, linear combinations, collisions, and transitions. The selection first elaborates on the fundamental principles of quantum mechanics, exactly soluble bound state problems, and continuum. Discussions focus on delta function normalization, spherically symmetric potentials, rectangular potential wells, harmonic oscillators, spherically symmetrical potentials, Coulomb potential, axiomatic basis, consequences of first three postulates, and time-dependent states. The text then examines the stationary perturbation theory, variational method, and the asymptotic approximation method. Concerns cover the application of the asymptotic approximation method to potential barrier problems, method of linear combinations, lower bounds for the ground state eigenenergy, relative degeneracy, and degenerate case. The publication examines the theory of collisions and transitions, including the scattering of identical particles, Coulomb field, methods of determining scattering phases, persistent perturbations, and adiabatic approximation. The selection is a valuable source of information for researchers interested in quantum theory.

Table of Contents


  • Contributors to this Volume

    Preface

    Contents of Volumes 10-II and 10-III

    Table of Atomic Units

    1. Preliminaries

    1. Historical Survey

    2. Differential Operators

    3. Matrices

    4. Equivalence of Differential Operators and Matrices

    References

    2. Fundamental Principles of Quantum Mechanics

    1. General Definitions

    2. Axiomatic Basis

    3. Consequences of First Three Postulates

    4. The Properties of Angular Momentum Derived by Matrix Methods

    5. Time-Dependent States

    References

    Appendix 1. The Dirac δ-Function

    1. Closure of a Complete Orthonormal Set

    2. Transformation Theory

    Appendix 2. Eigenstates and Eigenvalues of the Electron Spin

    3. Exactly Soluble Bound State Problems

    1. Rectangular Potential Wells

    2. Harmonic Oscillators

    3. System of Two Particles

    4. Spherically Symmetrical Potentials

    5. The Coulomb Potential

    6. Two-Centre Coulomb Potentials

    7. Momentum Wave Functions

    References

    Appendix 1. Hermite Polynomials

    Appendix 2. Legendre Polynomials and Spherical Harmonics

    Associated Legendre Polynomials

    Appendix 3. Laguerre Polynomials

    Associated Laguerre Polynomials

    Appendix 4. Spherical Bessel Functions

    4. The Continuum

    1. Free Particle. Energy Wave Functions

    2. Delta Function Normalization

    3. Spherically Symmetric Potentials

    References

    Appendix. Coulomb Wave Functions

    5. Stationary Perturbation Theory

    1. The Rayleigh-Schrödinger Perturbation Theory

    2. The Nondegenerate Case

    3. The Degenerate Case

    4. Perturbation Theory in Matrix Form

    5. Reduction of the Degenerate Case to the Nondegenerate

    6. Relative Degeneracy

    7. The Lennard-Jones-Brillouin-Wigner Series Expansion

    References

    6. The Variational Method

    1. The Rayleigh-Ritz Variational Method

    2. Lower Bounds for the Ground State Eigenenergy

    3. Method of Linear Combinations

    4. Two-Electron Systems

    5. The Virial Theorem

    References

    7. The Asymptotic Approximation (AA) Method

    1. History and Description of the Method

    2. Applications of the Method to Potential Well Problems

    3. Application of the Method to Potential Barrier Problems

    4. Radial Problems

    References

    8. Transitions

    1. Variation of Constants

    2. Transient Perturbations

    3. Persistent Perturbations

    4. Sudden Approximation

    5. Time-Independent and Harmonic Perturbations

    6. Adiabatic Approximation

    References

    9. Theory of Collisions

    1. Classical Considerations

    2. Quantum Theory of Scattering by a Centre of Force

    3. Applications of Preceding Theory

    4. Methods of Determining Scattering Phases

    5. Non-Coulomb Field

    6. Coulomb Field

    7. Scattering of Identical Particles

    8. Use of Variation Methods in the Solution of Scattering Problems

    9. Scattering by a Spin Dependent Interaction

    10. General Collision Theory

    11. Inelastic Collisions

    12. Application of Quantum Collision Theory to the Scattering of Electrons by Atoms

    13. Application of Quantum Collision Theory to Problems of Nuclear Physics

    References

    Author Index

    Subject Index

Product details

  • No. of pages: 464
  • Language: English
  • Copyright: © Academic Press 1961
  • Published: January 1, 1961
  • Imprint: Academic Press
  • eBook ISBN: 9781483275888

About the Editor

D. R. Bates

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