Quantum Theory

Elements

1st Edition - January 1, 1961

Editor: D. R. Bates

eBook ISBN:

9 7 8 - 1 - 4 8 3 2 - 7 5 8 8 - 8

Quantum Theory: A Treatise in Three Volumes, I: Elements focuses on the principles, methodologies, and approaches involved in quantum theory, including quantum mechanics, linear… Read more

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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.

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