In the period between the birth of quantum mechanics and the late 1950s, V.A. Fock wrote papers that are now deemed classics. In his works on theoretical physics, Fock not only skillfully applied advanced analytical and algebraic methods, but also systematically created new mathematical tools when existing approaches proved insufficient.
This collection of Fock's papers published in various sources between 1923 and 1959 in Russian, German, French, and English. These papers explore some of the fundamental notions of theoretical quantum physics, such as the Hartree-Fock method, Fock space, the Fock symmetry of the hydrogen atom, and the Fock functional method. They also present Fock's views on the interpretation of quantum mechanics and the fundamental significance of approximate methods in theoretical physics.
V.A. Fock was a key contributor to one of the most exciting periods of development in 20th-century physics, and this book conveys the essence of that time. The seminal works presented in this book are a helpful reference for any student or researcher in theoretical and mathematical physics, especially those specializing in quantum mechanics and quantum field theory.
Author(s): V.A. Fok
Publisher: CRC Press
Year: 2004
Language: English
Pages: 580
tf1607fm
Selected Works V.A. Fock: Quantum Mechanics and Quantum Field Theory
Contents
Preface
The following abbreviations are used for the titles of Russian editions
TF1607ch23-1
Table of Contents file://TF1607fm.pdf Chapter 23-1: On Rayleigh's Pendulum
1 The General Method. Establishing the Differential Equations of the Problem
2 Integration of the Differential Equations (*)
3 Equation of Motion for the Angle…. Its Integration
4 The Adiabatic Invariance of…
TF1607ch26-1
Table of Contents file://TF1607fm.pdf Chapter 26-1: On Schrödinger's Wave Mechanics
Part I
Part II
1 The Kepler Motion in Magnetic Field
2 The Motion of an Electron in the Electrostatic Field of the Nucleus and in the Magnetic Field of the Dipole which Coincides with the Nucleus
3 The Relativistic Kepler Motion
4 The Stark Effect
References
TF1607ch26-2
Table of Contents file://TF1607fm.pdf Chapter 26-2: On the Invariant Form of the Wave Equation and of the Equations of Motion for a Charged Massive Point
1 The special relativity
2 The General Relativity
TF1607ch28-1
Table of Contents file://TF1607fm.pdf Chapter 28-1: A Comment on Quantization of the Harmonic Oscillator in a Magnetic Field
References
TF1607ch28-2
Table of Contents file://TF1607fm.pdf Chapter 28-2: On the Relation between the Integrals of the Quantum Mechanical Equations of Motion and the Schrödinger Wave Equation
Appendix: The normalization of the eigenfunctions of the operators depending on time explicitly
TF1607ch28-3
Table of Contents file://TF1607fm.pdf Chapter 28-3: Generalization and Solution of the Dirac Statistical Equation
References
TF1607ch28-4
Table of Contents file://TF1607fm.pdf Chapter 28-4: Proof of the Adiabatic Theorem
Appendix: Proof of the Lemma in…
List of Papers on the Adiabatic Theorem in Quantum Mechanics
TF1607ch29-1
Table of Contents file://TF1607fm.pdf Chapter 29-1: On “Improper" Functions in Quantum Mechanics
References
TF1607ch29-2
Table of Contents file://TF1607fm.pdf Chapter 29-2: On the Notion of Velocity in the Dirac Theory of the Electron
Appendix: Eigenvalues spectrum of the four-speed operator
TF1607ch29-3
Table of Contents file://TF1607fm.pdf Chapter 29-3: On the Dirac Equations in General Relativity
TF1607ch29-4
Table of Contents file://TF1607fm.pdf Chapter 29-4: Dirac Wave Equation and Riemann Geometry
1 Lorentz Transformations for a Semi-vector
2 Parallel Transport of a Semi-Vector in Riemann Geometry
3 Dirac Wave Equation
4 Energy Tensor
5 Equations of Motion in Quantum Mechanics
6 Conclusion
TF1607ch30-1
Table of Contents file://TF1607fm.pdf Chapter 30-1: A Comment on the Virial Relation
TF1607ch30-2
Table of Contents file://TF1607fm.pdf Chapter 30-2: An Approximate Method for Solving the Quantum Many-Body Problem
1 Introduction
2 The Idea of the Method
3 Example: A Helium Atom
4 Hartree's Equations
5 The Symmetry Properties of the Wave Function. Example: A Lithium Atom
6 The Derivation of Generalized Hartree’s Equations
7 Analysis of the Equations and a New Formulation of the Variational Principle
8 The Spectral Line Intensities
TF1607ch30-3
Table of Contents file://TF1607fm.pdf Chapter 30-3: Application of the Generalized Hartree Method to the Sodium Atom
1 A Form of Wave Functions
2 Expressions for the Energy of an Atom
3 Variational Equations
4 Properties of the Coefficients of the Equations
5 Calculation of Terms
6 Intensities
TF1607ch30-4
Table of Contents file://TF1607fm.pdf Chapter 30-4: New Uncertainty Properties of the Electromagnetic Field
Electric Field Intensities
Magnetic Field Intensities
Another Form of Relations (1) and (2)
Concluding Remarks
TF1607ch30-5
Table of Contents file://TF1607fm.pdf Chapter 30-5: The Mechanics of Photons
TF1607ch32-1
Table of Contents file://TF1607fm.pdf Chapter 32-1: A Comment on the Virial Relation in Classical Mechanics
TF1607ch32-2
Table of Contents file://TF1607fm.pdf Chapter 32-2: Configuration Space and Second Quantization
I Transition From the Configuration Space to Second Quantization
Bose Statistics
Fermi Statistics
II Representation of Operators psi in Configuration Space
Time Dependence of psi Operators and Quantized Wave Equation
Derivation of the Hartree Equation by the Second Quantization Method
TF1607ch32-3
Table of Contents file://TF1607fm.pdf Chapter 32-3: On Dirac's Quantum Electrodynamics
TF1607ch32-4
Table of Contents file://TF1607fm.pdf Chapter 32-4: On Quantization of Electro-magnetic Waves and Interaction of Charges in Dirac Theory
I Quantization of Electro-Magnetic Fields
II Application to the Schrödinger Equation
III Application to the Dirac Equation
References
TF1607ch32-5
Table of Contents file://TF1607fm.pdf Chapter 32-5: On Quantum Electrodynamics
Part I Equivalence of Dirac's and Heisenberg-Pauli's Theories
Part II The Maxwellian Case
References
TF1607ch33-1
Table of Contents file://TF1607fm.pdf Chapter 33-1: On the Theory of Positrons
1 Definition of States with Negative Energy
2 Quantized Wave Function
3 Transformation of the Quantized Operator
4 The System of Equations in the Configuration Space
TF1607ch33-2
Table of Contents file://TF1607fm.pdf Chapter 33-2: On Quantum Exchange Energy
1 One-body Problem with Quantum Exchange
2 Schrödinger Equation
3 Classical Analog of Quantum Exchange Energy
4 Dirac Equation
TF1607ch34-1
Table of Contents file://TF1607fm.pdf Chapter 34-1: On the Numerical Solution of Generalized Equations of the Self-consistent Field
1 Form of Equations
2 Method of Successive Approximations
3 Construction of the Initial Approximation
4 On the Stability of the Process of Numerical Integration
5 Properties of the Generalized Green's Function and Its Construction
6 Comments on the Numerical Integration of Equations
7 Some Numerical Results for Sodium
TF1607ch34-2
Table of Contents file://TF1607fm.pdf Chapter 34-2: An Approximate Representation of the Wave Functions of Penetrating Orbits
References
TF1607ch34-3
Table of Contents file://TF1607fm.pdf Chapter 34-3: On Quantum Electrodynamics
Introduction
I Introducing the Functionals for the Case of Bose Statistics
II Electrodynamics of Vacuum
On the Measurability of the Fourier Components for the Field
III Interaction with Matter. Initial Equations
Eliminating the Supplementary Conditions
The Wave Equation in the Case of Coinciding Times
Equations in the Momentum Space of Light Quanta
Some Applications
TF1607ch35-1
Table of Contents file://TF1607fm.pdf Chapter 35-1: Hydrogen Atom and Non-Euclidean Geometry
References
TF1607ch35-2
Table of Contents file://TF1607fm.pdf Chapter 35-2: Extremal Problems in Quantum Theory
1 Introduction
2 Description of Physical Quantities
3 Construction of Quantum Operators
4 Examples of Physical Interpretations of Operators
5 Statistical Interpretation of the Fundamental Functions
6 Conclusion
TF1607ch36-1
Table of Contents file://TF1607fm.pdf Chapter 36-1: The Fundamental Significance of Approximate Methods in Theoretical Physics
References
TF1607ch37-1
Table of Contents file://TF1607fm.pdf Chapter 37-1: The Method of Functionals in Quantum Electrodynamics
Introduction
1 Description of a System with Indefinite Number of Particles by Functionals
a) Functionals and quantized operators
b) Conjugacy of operators b(k) and b†(k) their properties
2 Quantum Electrodynamics
a) Basic ideas
b) Energy of the light field
c) Field quantization
d) Basic equation of quantum electrodynamics
TF1607ch37-2
Table of Contents file://TF1607fm.pdf Chapter 37-2: Proper Time in Classical and Quantum Mechanics
I Classical Mechanics
II Proper Time in the Dirac Equation
III Applications to the Positron Theory
References
TF1607ch40-1
Table of Contents file://TF1607fm.pdf Chapter 40-1: Incomplete Separation of Variables for Divalent Atoms
1 Construction of the Wave Function
Introduction
2 Calculation of Density Integral
Introduction
3 Dependence of Wave Functions on Spin
Introduction
4 Determination of Dependence on Spin Variables in the Matrix Elements of the Electron Density
Introduction
5 Expression for the Energy of the Atom and Equations for Wave Functions
Introduction
References
TF1607ch40-2
Table of Contents file://TF1607fm.pdf Chapter 40-2: On the Wave Functions of Many-Electron Systems
Introduction
1 Spin and General Expression of its Eigenfunctions
2 The Symmetry Properties of the Schrödinger Wave Function
3 Expression for Functions with Spin by Means of the Schrödinger Function
4 The Case of Spherical Symmetry
Supplement The mixed density in terms of wave functions
References
TF1607ch43-1
Table of Contents file://TF1607fm.pdf Chapter 43-1: On the Representation of an Arbitrary Function by an Integral Involving Legendre's Function with a Complex Index
TF1607ch47-1
Table of Contents file://TF1607fm.pdf Chapter 47-1: On the Uncertainty Relation between Time and Energy
Introduction
1 Relation Referring to the Measurement Act
2 Relation Referring to the Motion of a Wave Packet
3 Comparison of Bohr's Relation with That of Mandelstam
4 Connection between the Energy Distribution Function and the Law of Decay of a Given State
Appendix: The energy distribution function in the problem of the potential well
References
TF1607ch50-1
Table of Contents file://TF1607fm.pdf Chapter 50-1: Application of Two-Electron Functions in the Theory of Chemical Bonds
References
TF1607ch54-1
Table of Contents file://TF1607fm.pdf Chapter 54-1: On the Schrödinger Equation of the Helium Atom
1 The Hylleraas Equation and its Transformation
2 The Equations of Laplace and Poisson on a Four-dimensional Sphere
3 Solution of the Hylleraas Equation for Finite Values of R
4 The Behavior of the Solution for Unlimited Values of R
References
TF1607ch57-1
Table of Contents file://TF1607fm.pdf Chapter 57-1: On the Interpretation of Quantum Mechanics
1 Attempts of Classical Interpretation of the Wave Function and the Causes of their Inconsistency
2 Niels Bohr's Ideas and His Terminology
3 Rejection of New Ideas as a Reaction to Their Positivistic Interpretation
4 Relativity to the Observation Tools
5 The Notion of a Device
6 The Essence of the Wave-Particle Dualism
7 Probabilistic Description of the Interaction between an Object and a Device
8 Probabilistic Characteristic of the State of an Object
9 The Notions of Potentially Possible and Actual in Classical Physics
10 Probability and Statistics in Quantum Mechanics
11 Forms of Expression of the Causality Principle in Quantum Mechanics
12 Philosophical Questions Put Forward by Quantum Mechanics
TF1607ch59-1
Table of Contents file://TF1607fm.pdf Chapter 59-1: On the Canonical Transformation in Classical and Quantum Mechanics
