Fundamentals Of Quantum Mechanics | |
---|---|
Original Title | Fundamentals Of Quantum Mechanics |
Author | V. A. Fock |
Publication date |
1986 |
Topics | quantum mechanics, Schrodinger equation, pauli electron, dirac electron, field theory, mir publishers, physics, wave equation, perturbation, atom, energy levels, zeeman effect, stark effect, matrix mechanics, electron |
Collection | mir-titles, additional_collections |
Language | English |
Book Type | EBook |
Material Type | Book |
File Type | |
Downloadable | Yes |
Support | Mobile, Desktop, Tablet |
Scan Quality: | Best No watermark |
PDF Quality: | Good |
Availability | Yes |
Price | 0.00 |
Submitted By | mirtitles |
Submit Date | |
This unique course in quantum mechanics was written by
For the second Russian edition the author has revised Foreword 5 Preface to the First Russian Edition 8 PART I BASIC CONCEPTS OF QUANTUM MECHANICS Chapter I. The physical and epistemological bases of quantum mechanics 13 I. The need for new methods and concepts in describing atomic pheno- 3. Range of application of the classical way of describing phenomena 4. Relativity with respect to the means of observation as the basis for Chapter II. The mathematical apparatus of quantum mechanics 22 I. Quantum mechanics and the linear-operator problems 22 tion into the independent variable 32 tions 37 I. Interpretation of the eigenvalues of an operator 41 10. An example of canonical transformation 63 9 10 14. Contents Heisenberg’s matrices 73 Chapter IV. The probabilistic interpretation of quantum mechanics 85 1. Mathematical exprctation in the probability theory 85
Chapter I. The Schriidlnger equation. The harmonic oscillator 96 I. Equations of motion and the wave equation 96 problem 106 theory 112 classical mechanics I15 I. Statement of the problem 119
Chapter III. Radiation, the theory of dispersion, and the law of decay 137 I. Classical formulas 137 2. Charge density and current density 139 3. Frequencies and intensities 143 4. Intensities in a continuous spectrum 146 5. Perturbation of an atom by a light wave 148 6. The dispersion formula 150 7. Penetration of a potential barrier by a particle 153 8. The law of decay of a quasi-stationary state 156 Contents 11 1. General remarks 160 2. Conservation of angular momentum 161 3. Operators in spherical coordinates. Separation of variables 164 4. Solution of the differential equation for spherical harmonics 166 5. Some properties of spherical harmonics 170 6. Normalized spherical harmonics 173 7. The radial functions. A general survey 175 8. Description of the states of a valence electron. Quantum numbers 179 9. The selection rule 181 Chapter V. The Coulomb field 188 1. General remarks 188 2. The radial equation for the hydrogen atom. Atomic units 188 3. Solution of an auxiliary problem 190 4. Some properties of generalized Laguerre polynomials 193 5. Eigenvalues and eigenfunctions of the auxiliary problem 197 6. Energy levels and radial functions for the discrete hydrogen spectrum 198 7. Solution of the differential equation for the continuous spectrum in the form of a definite integral 201 8. Derivation of the asymptotic expression 204 9. Radial functions for the continuous hydrogen spectrum 207 10. Intensities in the hydrogen spectrum 211 11. The Stark effect. General remarks 215 12. The Schr5dinger equation in parabolic coordinates 216 13. Splitting of energy levels in an electric field 219 14. Scattering of a.-particles. Statement of the problem 221 15. Solution of equations 223 16. The Rutherford·scattering law 225 17. The virial theorem in classical and in quantum mechanics 226 18. Some remarks concerning the superposition principle and the probabilistic interpretation of the wave function 229 PART III 1. The electron angular momentum 232 2. The operators of total angular momentum in spherical coordinates 236 3. Spherical harmonics with spin 239 4. Some properties of spherical harmonics with spin 243 5. The Pauli wave equation 245 6. Operator P in spherical and cylindrical coordinates and its relation to .A 248 7. An electron in a magnetic field 254 PART IV THE MANY-ELECTRON PROBLEM OF QUANTUM MECHANICS 1. Symmetry properties of the wave function 257 2. The Hamiltonian and its symmetry 262 3. The self-consistent field method 263 4. The equation for the valence electron and the operator of quantum 5. The self-consistent field method in the theory of atoms 271 6. The symmetry of the Hamiltonian of a hydrogen·like atom 276 PART V DIRAC’S THEORY OF THE ELECTRON I. Quantum mechanics and the theory of relativity 281 2. Classical equations of motion 281 3. Derivation of the wave equation 283 4. The Dirac matrices 284 5. The Dirac equation for a free electron 288 6. Lorentz transformations 291 7. Form of matrix S for spatial rotations of axes and for Lorentz transformations 293 8. Current density 297 9. The Dirac equation in the case of a field. Equations of motion 298 10. Angular momentum and the spin vector in Dirac’s theory 301 11. The kinetic energy of an electron 304 12. The second intrinsic degree of freedom of the electron 305 13. Second-order equations 308 Chapter II. The use of the Dirac equation In physical problems 312 I. The free electron 312 2. An electron in a homogeneous magnetic field 316 3. Constants of the motion in the problem with spherical symmetry 320 4. Generalized spherical harmonics 322 5. The radial equation 325 6. Comparison with the SchrOdinger equation 327 7. General investigation of the radial equations 329 8. Quantum numbers 334 9. Heisenberg’s matrices and the selection rule 336 10. Alternative derivation of the selection rule 340 11. The hydrogen atom. Radial functions 343 13. The Zeeman effect. Statement of the problem 350 14. Calculation of the perturbation matrix 352 15. Splitting of energy levels in a magnetic field 355 Chapter III. On the theory of positrons 359 I. Charge conjugation 359 2. Basic ideas of positron theory 360 3. Positrons as unfilled states 361 Index 362 |