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The book was translated from the Russian by G. Leib. The book was first published in 1982, revised from the 1977 Russian edition by Mir Publishers. The present book is the second volume of a guide to theoretical physics. As in the first Volume I have adhered to the rule of omitting what is explained in sufficient detail in modern general courses of physics. In particular, the experimental fundamentals of quantum physics are not discussed. With a view to the fact that the mastering of the mathematical apparatus of quantum mechanics involves great difficulties, I have done everything in my power to make calculations as simple and as clear as possible. For this purpose, special care was taken in choosing the notation. The book is provided with mathematical appendices. Sometimes I refer to the mathematical appendices of Volume 1. The book has been conceived first of all as a training aid for students of non-theoretical specialities of higher educational establishments. Acquaintance with it will facilitate a more detailed studying of the subject with the aid of fundamental guides.
Preface
Foundations of Quantum Mechanics
Introduction
State
The Superposition Principle
The Physical Meaning of the Psi-Function
The Schrodinger Equation
Probability Flux Density
Mathematical Tools of Quantum Mechanics
Fundamental Postulates
Linear Operators
Matrix Representation of Operators
The Algebra of Operators
The Uncertainty Relation
The Continuous Spectrum
Dirac Notation
Transformation of Functions and Operators from One Representation to Another
Eigenvalues and Eigenfunctions of Physical Quantities
Operators of Physical Quantities
Rules for Commutation of Operators of Physical Quantities
Eigenfunctions of the Coordinate and Momentum Operators
Momentum and Energy Representation
Eigenvalues and Eigenfunctions of tho Angular Momentum Operator
Parity
Time Dependence of Physical Quantities
The Time Derivative of an Operator
Time Dependence of Matrix Elements
Motion of a Particle in Force Fields
A Particle in a Central Force Field
An Electron in a Coulomb Field. The Hydrogen Atom
The Harmonic Oscillator
Solution of the Harmonic Oscillator Problem in the Matrix Form
Annihilation and Creation Operators
Perturbation Theory
Introduction
Time-Independent Perturbations
Case of Two Close Levels
DegenerateCase
Examples of Application of tho Stationary Perturbation Theory
Time-Dependent Perturbations
Perturbations Varying Harmonically with Time
Transitions in a Continuous Spectrum
Potential Energy as a Perturbation
The Quasiclassical Approximation
The Classical Limit
Boundary Conditions at a Turning Point
Bohr-Sommerfeld Quantization Rule
Penetration of a Potential Barrier
Semiempirical Theory of Particles with Spin
Psi-Function of a Particle with Spin
Spin Operators
Eigenvalues and Eigenfunctions of Spin Operators
Spinors 205
Systems Consisting of Identical Particles
Principle of Indistinguishability of Identical Particles
Psi-Functions for Systems of Particles. The Pauli Principle
Summation of Angular Momenta
Psi-Function of System of Two Particles Having a Spin of 1/2
Exchange Interaction
Second Quantization
Second Quantization Applied to Bosons
Second Quantization Applied to Fermions
Atoms and Molecules
Methods of Calculating Atomic Systems
The Helium Atom
The Variation Method
The Method or the Self-Consistent Field
The Thomas-Fermi Method
The Zeeman Effect
The Theory of Molecules in the Adiabatic Approximation
The Hydrogen Molecule
Radiation Theory 291
Quantization of an Electromagnetic Field
Interaction of an Electromagnetic Field with a Charged Particle
One-Photon Processes
Dipole Radiation
Selection Rules
Scattering Theory
Scattering Cross Section
Scattering Amplitude
Born Approximation
Method of Partial Waves
Inelastic Scattering
Appendices
Angular Momentum Operators in Spherical Coordinates
Spherical Functions
Chebyshev-Hermite Polynomials
Some Information from the Theory of Functions of a Complex Variable
Airy Function
Method of Green's Functions
Solution of the Fundamental Equation of the Scattering Theory by the Method of Green's Functions
The Dirac Delta Function
Index