Quantum Mechanics by L.D. Landau; E.M. Lifshitz in pdf

 Quantum Mechanics by L.D. Landau; E.M. Lifshitz in pdf

this is the book Quantum Mechanics in pdf written  by L.D. Landau; E.M. Lifshitz , published by University Reprints ,2019  of professors of  science faculties  universities  .

   

Information about the book

Language of the book: English language

Book Title: Quantum Mechanics

Scriptwriter: by L.D. Landau; E.M. Lifshitz

Year of printing:   University Reprints ,2019

File Format:PDF

Number of chapters: 15 CHAPTER

Number of pages: 632 pages

File Size: 10,70 MB

Contents

Notation xiii I. THE BASIC CONCEPTS OF QUANTUM MECHANICS

§1. The uncertainty principle 1

§2. The principle of superposition 6

§3. Operators 8

§4. Addition and multiplication of operators 13

§5. The continuous spectrum 15

§6. The passage to the limiting case of classical mechanics 20

§7. The wave function and measurements 21

II. ENERGY AND MOMENTUM

§8. The Hamiltonian operator 25

§9. The differentiation of operators with respect to time 26

§10. Stationary states 27

§11. Matrices 30

§12. Transformation of matrices 35

§13. The Heisenberg representation of operators 37

§14. The density matrix 38

§15. Momentum 41

§16. Uncertainty relations 46

III. SCHRODINGER'S EQUATION

§17. Schrodinger's equation 50

§18. The fundamental properties of Schrodinger's equation 53

§19. The current density 55

§20. The variational principle 58

§21. General properties of motion in one dimension 60

§22. The potential well 63

§23. The linear oscillator 67

§24. Motion in a homogeneous field 73

§25. The transmission coefficient 75

IV. ANGULAR MOMENTUM

§26. Angular momentum 81

§27. Eigenvalues of the angular momentum 85

§28. Eigenfunctions of the angular momentum 88

§29. Matrix elements of vectors 91

§30. Parity of a state 95

§31. Addition of angular momenta 97

V. MOTION IN A CENTRALLY SYMMETRIC FIELD Page

§32. Motion in a centrally symmetric field 101

§33. Free motion (spherical polar co-ordinates) 104

§34. Resolution of a plane wave 111

§35. "Fall" of a particle to the centre 113

§36. Motion in a Coulomb field (spherical polar co-ordinates) 116

§37. Motion in a Coulomb field (parabolic co-ordinates) 125

VI. PERTURBATION THEORY

§38. Perturbations independent of time 129

§39. The secular equation 133

§40. Perturbations depending on time 136

§41. Transitions under a perturbation acting for a finite time 140

§42. Transitions under the action of a periodic perturbation 146

§43. Transitions in the continuous spectrum 147

§44. The uncertainty relation for energy 150

§45. Potential energy as a perturbation 153

VII. THE QUASI-CLASSICAL CASE

§46. The wave function in the quasi-classical case 158

§47. Boundary conditions in the quasi- classical case 161

§48. Bohr and Sommerfeld's quantisation rule 162

§49. Quasi-classical motion in a centrally symmetric field 167

§50. Penetration through a potential barrier 171

§51. Calculation of the quasi-classical matrix elements 177

§52. The transition probability in the quasi-classical case 181

§53. Transitions under the action of adiabatic perturbations 185

VIII. SPIN

§54. Spin 188

§55. Spinors 191

§56. Spinors of higher rank 196

§57. The wave functions of particles with arbitrary spin 198

§58. The relation between spinors and tensors 200

§59. Partial polarisation of particles 204

§60. Time reversal and Kramers' theorem 206

IX. IDENTITY OF PARTICLES

§61. The principle of indistinguishability of similar particles 209

§62. Exchange interaction 212

§63. Symmetry with respect to interchange 216

§64. Second quantisation. The case of Bose statistics 221

§65. Second quantisation. The case of Fermi statistics 227

X. THE ATOM

Page

§66. Atomic energy levels 231

§67. Electron states in the atom 232

§68. Hydrogen-like energy levels 236

§69. The self-consistent field 237

§70. The Thomas-Fermi equation 241

§71. Wave functions of the outer electrons near the nucleus 246

§72. Fine structure of atomic levels 247

§73. The periodic system of D. I. Mendeleev 252

§74. X-ray terms 259

§75. Multipole moments 261

§76. The Stark effect 265

§77. The Stark effect in hydrogen 269

XI. THE DIATOMIC MOLECULE

§78. Electron terms in the diatomic molecule 277

§79. The intersection of electron terms 279

§80. The relation between molecular and atomic terms 282

§81. Valency 286

§82. Vibrational and rotational structures of singlet terms in the diatomic

molecule 293

§83. Multiplet terms. Case a 299

§84. Multiplet terms. Case b 303

§85. Multiplet terms. Cases c and d 307

§86. Symmetry of molecular terms 309

§87. Matrix elements for the diatomic molecule 312

§88. A-doubling 316

§89. The interaction of atoms at large distances 319

§90. Pre-dissociation 322

XII. THE THEORY OF SYMMETRY

§91. Symmetry transformations 332

§92. Transformation groups 335

§93. Point groups 338

§94. Representations of groups 347

§95. Irreducible representations of point groups 354

§96. Irreducible representations and the classification of terms 358

§97. Selection rules for matrix elements 361

§98. Continuous groups 364

§99. Two-valued representations of finite point groups 367

XIV. ADDITION OF ANGULAR MOMENTA

§106. 3/-symbols 401

§107. Matrix elements of tensors 408

§108. 6/-symbols 412

§109. Matrix elements for addition of angular momenta 418

XV. MOTION IN A MAGNETIC FIELD

§110. Schrodinger's equation in a magnetic field 421

§111. Motion in a uniform magnetic field 424

§112. The Zeeman effect 427

§113. Spin in a variable magnetic field 434

§114. The current density in a magnetic field 435

XVI. NUCLEAR STRUCTURE

§115. Isotopic invariance 438

§116. Nuclear forces 442

§117. The shell model 447

§118. Non-spherical nuclei 456

§119. Isotopic shift 461

§120. Hyperfine structure of atomic levels 463

§121. Hyperfine structure of molecular levels 466

XVII. THE THEORY OF ELASTIC COLLISIONS

§122. The general theory of scattering 469

§123. An investigation of the general formula 472

§124. The unitary condition for scattering 475

§125. Born's formula 479

§126. The quasi-classical case 486

§127. Scattering at high energies 489

§128. Analytical properties of the scattering amplitude 492

§129. The dispersion relation 497

§130. The scattering of slow particles

§131. Resonance scattering at low energies 505

§132. Resonance at a quasi-discrete level 511

§133. Rutherford's formula 516

§134. The system of wave functions of the continuous spectrum 519

§135. Collisions of like particles 523

§136. Resonance scattering of charged particles 526

§137. Elastic collisions between fast electrons and atoms 531

§138. Scattering with spin-orbit interaction 535

XVIII. THE THEORY OF INELASTIC COLLISIONS

§139. Elastic scattering in the presence of inelastic processes 542

§140. Inelastic scattering of slow particles 548

§141. The scattering matrix in the presence of reactions 550

§142. Breit and Wigner's formula 554

§143. Interaction in the final state in reactions 562

§144. Behaviour of cross-sections near the reaction threshold 565

§145. Inelastic collisions between fast electrons and atoms 571

§146. The effective retardation 580

§147. Inelastic collisions between heavy particles and atoms 584

§148. Scattering by molecules 587

MATHEMATICAL APPENDICES

§a. Hermite polynomials 593

§b. The Airy function 596

§c. Legendre polynomials 598

§d. The confluent hypergeometric function 600

§e. The hypergeometric function 605

§f. The calculation of integrals containing confluent hypergeometric

functions ■ 607

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