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