Fundamentals of Quantum Mechanics

Front Cover
Front Jacket
Front Hard Cover
Title Page
FOREWORD
PREFACE TO THE SECOND RUSSIAN EDITION
PREFACE TO THE FIRST RUSSIAN EDITION
CONTENTS
Part I BASIC CONCEPTS OF QUANTUM MECHANICS
Chapter I THE PHYSICAL AND EPISTEMOLOGICAL BASES OF QUANTUM MECHANICS
1. The need for new methods and concepts in describing atomic phenomena
2. The classical description of phenomena
3. Range of application of the classical way of describing phenomena. Heisenberg's and Bohr's uncertainty relations
4. Relativity with respect to the meansof observation as the basis for the quantum way of describing phenomena
5. Potential possibility in quantum mechanics
Chapter II THE MATHEMATICAL APPARATUSOF QUANTUM MECHANICS
1. Quantum mechanics and the linear-operator problems
2. The operator concept and examples
3. Hermitian conjugate. Hermiticity
4. Operator and matrix multiplication
5. Eigenvalues and eigenfunctions
6. The Stieltjes integral and the operator corresponding to multiplication into the independent variable
7. Orthogonality of eigenfunctions and normalization
8. Expansion In eigenfunctions. Completeness property of eigenfunctions
Chapter III QUANTUM MECHANICAL OPERATORS
1. Interpretation of the eigenvalues of an operator
2. Poisson brackets
3. Position and momentum operators
4. Eigenfunctions and eigenvalues of the momentum operator
5. Quantum description of systems
6. Commutativity of operators
7. Angular momentum
8. The energy operator
9. Canonical transformation
10. An example of canonical transformation
11. Canonical transformation as an operator
12. Unitary Invariants
13. Time evolution of systems. Time dependence of operators
14. Heisenberg's matrices
15. Semiclassical approximation
16. Relation between canonical transformation and the contact transformation of classical mechanics
Chapter IV THE PROBABILISTIC INTERPRETATION OF QUANTUM MECHANICS
1. Mathematical expectation in the probability theory
2. Mathematical expectation in quantum mechanics
3. The probability formula
4. Time dependence of mathematical expectation
5. Correspondence between the theory of linear operators and the quantum theory
6. The concept of statistical ensemble In quantum mechanics
Part II SCHRODINGER'S THEORY
Chapter I THE SCHRODINGER EQUATION. THE HARMONIC OSCILLATOR.
1. Equations of motion and the wave equation
2. Constants of the motion
3. The Schrodinger equation for the harmonic oscillator
4. The one·dimensional harmonic oscillator
5. Hermite polynomials
6. Canonical transformation as illustratedby the harmonic-oscillator problem
7. Heisenberg's uncertainty relations
8. The time dependence of matrices. A comparison with the classical theory
9. An elementary criterion for the applicability of the formulas of classical mechanics
Chapter II PERTURBATION THEORY
1. Statement of the problem
2. Solution of the nonhomogeneous equation
3. Nondegenerate eigenvalues
4. Degenerate eigenvalues. Expansion in powers of the smallness parameter
5. The eigenfunctions in the zeroth-order approximation
6. The first and higher approximations
7. The case of adjacent eigenvalues
B. The anharmonic oscillator
Chapter III RADIATION, THE THEORY OF DISPERSION, AND THE LAW OF DECAY
1. Classical formulas
2. Charge density and current density
3. Frequencies and intensities
4. Intensities in a continuous spectrum
5. Perturbation of an atom by a light wave
6. The dispersion formula
8. The law of decay of a quasi-stationary state
7. Penetration of a potential barrier by a particle
Chapter IV AN ELECTRON IN A CENTRAL FIELD
1. General remarks
2. Conservation of angular momentum
3. Operators In spherical coordinates. Separation of variables
4. Solution of the differential equation for spherical harmonics
5. Some properties of spherical harmonics
6. Normalized spherical harmonics
7. The radial functions. A general survey
8. Description of the states of a valence electron. Quantum numbers
9. The selection rule
Chapter V THE COULOMB FIELD
1. General remarks
2. The radial equation for the hydrogen atom. Atomic units
3. Solution of an auxiliary problem
4. Some properties of generalized Laguerre polynomials
5. Eigenvalues and eigenfunctions of the auxiliary problem
6. Energy levels and radial functions for the discrete hydrogen spectrum
7. Solution of the differential equation for the continuous spectrum in the formof a definite integral
8. Derivation of the asymptotic expression
9. Radial functions for the continuous hydrogen spectrum
10. Intensities in the hydrogen spectrum
11. The Stark effect. General remarks
12. The Schrodinger equation in parabolic coordinates
13. Splitting of energy levels In an electric field
14. Scattering of a-partlcles. Statement of the problem
15. Solution of equations
16. The Rutherford scattering law
17. The virial theorem in classical and in quantum mechanics
18. Some remarks concerning the superposition principle and the probabilistic interpretation of the wave function
Part III PAULl'S THEORY OF THE ELECTRON
1. The electron angular momentum
2. The operators of total angular momentumin spherical coordinates
3. Spherical harmonics with spin
4. Some properties of spherical harmonics with spin
5. The Pauli wave equation
6. Operator P in spherical and cylindrical coordinates and its relation to M
7. An electron in a magnetic field
Part IV THE MANY-ELECTRON PROBLEM OF QUANTUM MECHANICS AND THE STRUCTURE OF ATOMS
1. Symmetry properties of the wave function
2. The Hamiltonian and Its symmetry
3. The self-consistent field method
4. The equation for the valence electron and the operator of quantum exchange
5. The self-consistent field method in the theory of atoms
6. The symmetry of the Hamiltonian of a hydrogen-like atom
Part V DIRAC'S THEORY OF THE ELECTRON
Chapter I THE DIRAC EQUATION
1. Quantum mechanics and the theory of relativity
2. Classical equations of motion
3. Derivation of the wave equation
4. The Dirac matrices
5. The Dirac equation for a free electron
6. Lorentz transformations
7. Form of matrix S for spatial rotationsof axes and for Lorentz transformations
8. Current density
9. The Dirac equation in the case of a field. Equations of motion
10. Angular momentum and the spin vector in Dirac's theory
11. The kinetic energy of an electron
12. The second intrinsic degree of freedom of the electron
13. Second-order equations
Chapter II THE USE OF THE DIRAC EQUATION IN PHYSICAL PROBLEMS
1. The free electron
2. An electron in a homogeneous magnetic field
3. Constants of the motion in the problem with spherical symmetry
4. Generalized spherical harmonics
5. The radial equation
6. Comparison with the Schrodinger equation
7. General investigation of the radial equations
8 Quantum numbers
9. Heisenberg's matrices and the selection rule
10. Alternative derivation of the selection rule
11. The hydrogen atom. Radial functions
12. Fine-structure levels of hydrogen
13. The Zeeman effect. Statement of the problem
14. Calculation of the perturbation matrix
15. Splitting of energy levels in a magnetic field
Chapter III ON THE THEORY OF POSITRONS
1. Charge conjugation
2. Basic ideas of positron theory
3. Positrons as unfilled states
INDEX
Back Hard Cover
Back Jacket
Back Cover