In this post we will see the two volume set titled Fundamentals of Theoretical Physics by I. V. Savelyev. Previously we have seen Physics A General Course by the same author.

The book being offered to the reader is a logical continuation of the author’s three-volume general course of physics. Everything possible has been done to avoid repenting what has been set out in the three-volume course. Particularly. the experiments underlying the advancing of physical ideas are not treated, and some of the results obtained are not discussed.

The book has been conceived as a training aid for students of non- theoretical specialities of higher educational institutions. I had in mind readers who would like to grasp the main ideas and methods of theoretical physics without delving into the details that are of interest only for a specialist. This book will be helpful for physics instructors at higher schools, and also for everyone interested in the subject but having no time to become acquainted with it (or re- store it in his memory) according to fundamental manuals.

The books were translated from the Russian by G. Leib and was first published in 1982.

We have added new covers to existing pdfs. All other credits to original uploaders. Thanks to commentators for points the libgen links.

Fundamentals of Theoretical Physics Vol 1

Fundamentals of Theoretical Physics Vol 2

Contents Vol 1

Part One. Mechanics 11 Chapter I. The Variational Principle in Mechanics 11 1. Introduction 11 2. Constraints 13 3. Equations of Motion in Cartesian Coordinates 16 4. Lagrange’s Equations in Generalized Coordinates 19 5. The’ Lagrangian and Energy 24 6. Examples of Compiling Lagrange’s Equations 28 7. Principle of Least Action 33 Chapter II. Conservation Laws 36 8. Energy Conservation 36 9. Momentum Conservation 37 10. Angular Momentum Conservation 39 Chapter III. Selected Problems in Mechanics 41 11. Motion of a Particle in a Central Force Field 41 12. Two-Body Problem 45 13. Elastic Collisions of Particles 49 14. Particle Scattering 53 15. Motion in Non-Inertial Reference Frames 57 Chapter IV. Small-Amplitude Oscillations 64 16. Free Oscillations of a System Without Friction 64 17. Damped Oscillations 66 18. Forced Oscillations 70 8 CONTENTS 19. Oscillations of a System with Many Degrees of Freedom 72 20. Coupled Pendulums 77 Chapter V. Mechanics of a Rigid Body 82 21. Kinematics of a Rigid Body 82 22. The Euler Angles 85 23. The Inertia Tensor 88 24. Angular Momentum of a Rigid Body 95 25. Free Axes of Rotation 99 26. Equation of Motion of a Rigid Body 101 27. Euler’s Equations 105 28. Free Symmetric Top 107 29. Symmetric Top in a Homogeneous Gravitational Field 111 Chapter VI. Canonical Equations 115 30. Hamilton’s Equations 115 31. Poisson Brackets 119, 32. The Hamilton- Jacobi Equation 121 Chapter VII. The Special Theory of Relativity 125 33. The Principle of Relativity 125 34. Interval 127 35. Lorentz Transformations 130 36. Four-Dimensional Velocity and Acceleration 134 37. Relativistic Dynamics 136 38. Momentum and Energy of a Particle 139 39. Action for a Relativistic Particle 143 40. Energy-Momentum Tensor 147 Part Two. Electrodynamics 157 Chapter VIII. Electrostatics 157 41. Electrostatic Field in a Vacuum 157 42. Poisson’s Equation 159 43. Expansion of a Field in Multipoles 161 44. Field in Dielectrics 166 45. Description of the Field in Dielectrics 170 46. Field in Anisotropic Dielectrics 175 Chapter IX. Magnetostatics 177 47. Stationary Magnetic Field in a Vacuum 177 48. Poisson’s Equation for the Vector Potential 179 49. Field of Solenoid 182 50. The Biot-Savart Law 186 51. Magnetic Moment 188 52. Field in Magnetics 194 Chapter X. Time-Varying Electromagnetic Field 199 53. Law of Electromagnetic Induction 199 CONTENTS 9 ’ 54. Displacement Current 200, 55. Maxwell’s Equations 201 56. Potentials of Electromagnetic Field 203 57. D’Alembert’s Equation 207 58. Density and Flux of Electromagnetic Field Energy 208 59. Momentum of Electromagnetic Field 211 Chapter XI. Equations of Electrodynamics in the Four-Dimensional Form 216 60. Four-Potential 216 61. Electromagnetic Field Tensor 219 62. Field Transformation Formulas 222 63. Field Invariants 225 64. Maxwell’s Equations in the Four-Dimensional Form 228 65. Equation of Motion of a Particle in a Field 230 Chapter XII. The Variational Principle in Electrodynamics 232 66. Action for a Charged Particle in an Electromagnetic Field 232 67. Action for an Electromagnetic Field 234 68. Derivation of Maxwell’s Equations from the Principle of Least Action 237 69. Energy-Momentum Tensor of an Electromagnetic Field 239 70. A Charged Particle in nil Electromagnetic Field 244 Chapter XIII. Electromagnetic Waves 248 71. The Wave Equation 248 72. A Plane Electromagnetic Wave in a Homogeneous and Isotropic Medium 250 73. A Monochromatic Plane Wave 255 74. A Plane Monochromatic Wave in a Conducting Medium 260 75. Non-Monochromatic Waves 265 Chapter XIV. Radiation of Electromagnetic Waves 269 76. Retarded Potentials 269 77. Field of a Uniformly Moving Charge 272 78. Field of an Arbitrarily Moving Charge 276 79. Field Produced by a System of Charges at Great Distances 288 80. Dipole Radiation 288 81. Magnetic Dipole and Quadrupole Radiations 291 Appendices 297 I. Lagrange’s Equations for a Holonomic System with Ideal Xon- Stationarv Constraints 297 II. Euler’s Theorem for Homogeneous Functions 299 III. Some Information from the Calculus of Variations 300 IV. Conics 309 V. Linear Differential Equations with Constant Coefficients 313 VI. Vectors 316 VII. Matrices 330 VIII. Determinants 338 IX. Quadratic Forms 347 10 CONTENTS X. Tensors 355 XI. Basic Concepts of Vector Analysis 370 XII. Four-Dimensional Vectors and Tensors i Space 393 XIII. The Dirac Delta Function 412 XIV. The Fourier Series and Integral 413 Index 419

Contents Volume 2

Chapter I. Foundations of Quantum Mechanics 9 1. Introduction 9 2. State 10 3. The Superposition Principle 12 4. The Physical Meaning of the Psi-Function 14 5. The Schrodinger Equation 16 6. Probability Flux Density 20 Chapter II. Mathematical Tools of Quantum Mechanics 23 7. Fundamental Postulates . 23 8. Linear Operators 27 9. Matrix Representation of Operators 31 10. The Algebra of Operators 38 11. The Uncertainty Relation 45 12. The Continuous Spectrum 48 13. Dirac Notation 51 14. Transformation of Functions and Operators from One Representa- tion to Another 55 Chapter III. Eigenvalues and Eigenfunctions of Physical Quantities 63 15. Operators of Physical Quantities 63 16. Rules for Commutation of Operators of Physical Quantities … 67 17. Eigenfunctions of the Coordinate and Momentum Operators … 71 18. Momentum and Energy Represonlal ions 74 19. Eigenvalues and Eigenfunctions of the Angular Momentum Operator 78 20. Parity 81 Chapter IV. Time Dependence of Physical Quantities 83 21. The Time Derivative of an Operator 83 22. Time Dependence of Matrix Elements 86 Chapter V. Motion of a Particle in Force Fields 89 23. A Particle in a Central Force Field 89 24. An Electron in a Coulomb Field. The Hydrogen Atom 94 25. The Harmonic Oscillator 106 26. Solution of the Harmonic Oscillator Problem in the Matrix Form 109 27. Annihilation and Creation Operators 116 CONTENTS 7 Chapter VI. Perturbation Theory 123 28. Introduction 123 29. Time-Independent Perturbations 123 30. Case of Two Close Levels 132 31. Degenerate Case 136 32. Examples of Application of the Stationary Perturbation Theory 141 33. Time-Dependent Perturbations 148 34. Perturbations Varying Harmonically with Time 156 35. Transitions in a Continuous Spectrum 163 36. Potential Energy as a Perturbation 164 Chapter VII. The Quasiclassical Approximation 169 37. The Classical Limit 169 38. Boundary Conditions at a Turning Point 174 39. Bohr-Sommerfeld Quantization Rule 184 40. Penetration of a Potential Barrier 188 Chapter VIII. Semiempirical Theory of Particles with Spin 192 41. Psi-Function of a Particle with Spin 192 42. Spin Operators 194 43. Eigenvalues and Eigenfunctions of Spin Operators 202 44. Spinors 205 Chapter IX. Systems Consisting of Identical Particles 214 45. Principle of Indistinguishability of Identical Particles 214 46. Psi-Functions for Systems of Particles. The Pauli Principle . . . 216 47. Summation of Angular Momenta 222 48. Psi-Function of System of Two Particles Having a Spin of 1/2 . . 225 49. Exchange Interaction 229 50. Second Quantization 233 51. Second Quantization Applied to Bosons 235 52. Second Quantization Applied to Fermions 250 Chapter X. Atoms and Molecules 258 53. Methods of Calculating Atomic Systems . 258 54. The Helium Atom f Ai 259 55. The Variation Method 263 56. The Method of the Self-Consistent Field 268 57. The Thomas-Fcrmi Method 275 58. The Zeeman Effect 278 59. The Theory of Molecules in the Adiabatic Approximation . . . 281 60. The Hydrogen Molecule 285 Chapter XI. Radiation Theory • 291 / i u^ir^u 61. Quantization of an Electromagnetic Field L • 291 62. Interaction of an Electromagnetic Field with a Charged Particle 301 ■63. One-Photon Processes 305 64. Dipole Radiation 308 65. Selection Rules 312 8 CONTENTS Chapter XII. Scattering Theory 315 66. Scattering Cross Section . SPlAtur 1 . 315 67. Scattering Amplitude 317 68. Born Approximation 319 69. Method of Partial Waves 321 70. Inelastic Scattering 328 Appendices . . I. Angular Momentum Operators in Spherical Coordinates . . . II. Spherical Functions III. Cuebyshev-IIerinite Polynomials IV. Some Information from the Theory of Functions of a Complex Variable …. V. Airy Function VI. Method of Green’s Functions VII. Solution of the Fundamental Equation of the Scattering Theory by the Method of Green’s Functions VIII. The Dirac Delta Function