Quantum Mechanics by D.I. BlokhintsevQuantum Mechanics by D.I. Blokhintsev

Quantum Mechanics

byD.I. BlokhintsevEditorS. Sykes, M.j. Kearsley

Paperback | April 19, 2012

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The English translation of Osnovy kvantovol mekhaniki has been made from the third and fourth Russian editions. These contained a number of important additions and changes as compared with the first two editions. The main additions concern collision theory, and applications of quantum mechanics to the theory of the atomic nucleus and to the theory of elementary particles. The development of these branches in recent years, resulting from the very rapid progress made in nuclear physics, has been so great that such additions need scarcely be defended. Some additions relating to methods have also been made, for example concerning the quasiclassical approxi­ mation, the theory of the Clebsch-Gordan coefficients and several other matters with which the modern physicist needs to be acquainted. The alterations that have been made involve not only the elimination of obviously out-of-date material but also the refinement of various formulations and statements. For these refinements I am indebted to many persons who at different times have expressed to me their critical comments and suggestions. Particularly important changes have been made regarding the definition of a quantum ensemble in Section 14.
Title:Quantum MechanicsFormat:PaperbackDimensions:551 pagesPublished:April 19, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401097135

ISBN - 13:9789401097130

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Table of Contents

I. Foundations of Quantum Theory.- 1. Energy and momentum of light quanta.- 2. Experimental test of the laws of conservation of energy and momentum for light quanta.- 3. Atomism.- 4. Bohr's theory.- 5. The elementary quantum theory of radiation.- 6. Black-body radiation.- 7. De Broglie waves. The group velocity.- 8. Diffraction of microparticles.- II. Foundations of Quantum Mechanics.- 9. Statistical interpretation of de Broglie waves.- 10. The position probability of a microparticle.- 11. The principle of superposition of states.- 12. Momentum probability distribution of a microparticle.- 13. Mean values of functions of co-ordinates and functions of momenta.- 14. Statistical ensembles in quantum mechanics.- 15. The uncertainty relation.- 16. Illustrations of the uncertainty relation.- 17. The significance of the measuring apparatus.- III. Representation of Mechanical Quantities by Operators.- 18. Linear self-adjoint operators.- 19. The general formula for the mean value of a quantity and the mean square deviation.- 20. Eigenvalues and eigenfunctions of operators and their physical significance. 'Quantisation'.- 21. Fundamental properties of eigenfunctions.- 22. General method of calculating the probabilities of the results of measurement.- 23. Conditions for a simultaneous measurement of different mechanical quantities to be possible.- 24. Co-ordinate and momentum operators of a microparticle.- 25. The angular momentum operator of a microparticle.- 26. The energy operator and the Hamilton's function operator.- 27. The Hamiltonian.- IV. Change of State with Time.- 28. Schrödinger's equation.- 29. Conservation of number of particles.- 30. Stationary states.- V. Change of Mechanical Quantities with Time.- 31. Time derivatives of operators.- 32. Equations of motion in quantum mechanics. Ehrenfest's theorems.- 33. Integrals of the motion.- VI. The Relation Between Quantum Mechanics, Classical Mechanics and Optics.- 34. The transition from the quantum equations to Newton's equations.- 35. The transition from Schrödinger's time-dependent equation to the classical Hamilton-Jacobi equation.- 36. Quantum mechanics and optics.- 37. The quasiclassical approximation (the Wentzel-Kramers-Brillouin method).- VII. Basic Theory of Representations.- 38. Different representations of the state of quantum systems.- 39. Different representations of operators of mechanical quantities. Matrices.- 40. Matrices and operations on them.- 41. Determination of the mean value and spectrum of a quantity represented by an operator in matrix form.- 42. Schrödinger's equation and the time dependence of operators in matrix form.- 43. Unitary transformations.- 44. The unitary transformation from one instant to another.- 45. The density matrix.- VIII. Theory of the Motion of Microparticles in a Field of Potential Forces.- 46. Introductory remarks.- 47. A harmonic oscillator.- 48. An oscillator in the energy representation.- 49. Motion in the field of a central force.- 50. Motion in a Coulomb field.- 51. The spectrum and wave functions of the hydrogen atom.- 52. Motion of an electron in univalent atoms.- 53. Currents in atoms. The magneton.- 54. Quantum levels of the diatomic molecule.- 55. Motion of an electron in a periodic field.- IX. Motion of a charged Microparticle in an Electromagnetic Field.- 56. An arbitrary electromagnetic field.- 57. Motion of a free charged particle in a uniform magnetic field.- X. Intrinsic Angular Momentum and Magnetic Moment of the Electron. Spin.- 58. Experimental proofs of the existence of electron spin.- 59. The electron spin operator.- 60. Spin functions.- 61. Pauli's equation.- 62. Splitting of spectral lines in a magnetic field.- 63. Motion of the spin in a variable magnetic field.- 64. Properties of the total angular momentum.- 65. Labelling of atomic terms having regard to the electron spin. Multiplet structure of spectra.- XI. Perturbation Theory.- 66. Statement of the problem.- 67. Perturbation in the absence of degeneracy.- 68. Perturbation in the presence of degeneracy.- 69. Splitting of levels in the case of twofold degeneracy.- 70. Comments on the removal of degeneracy.- XII. Simple Applications of Perturbation Theory.- 71. The anharmonic oscillator.- 72. Splitting of spectral lines in an electric field.- 73. Splitting of spectral lines of the hydrogen atom in an electric field.- 74. Splitting of spectral lines in a weak magnetic field.- 75. A diagrammatic interpretation of the splitting of levels in a weak magnetic field (the vector model).- 76. Perturbation theory for the continuous spectrum.- XIII. Collision Theory.- 77. Statement of the problem in collision theory of microparticles.- 78. Calculation of elastic scattering by the Born approximation.- 79. Elastic scattering of fast charged microparticles by atoms.- 80. The exact theory of scattering. The phase shift of the scattered waves and the cross-section.- 81. The general case of scattering.- 82. Scattering of a charged particle in a Coulomb field.- XIV. Theory of Quantum Transitions.- 83. Statement of the problem.- 84. Transition probabilities under a time-dependent perturbation.- 85. Transitions due to a time-independent perturbation.- XV. Emission, Absorption and Scattering of Light by Atomic Systems.- 86. Introductory remarks.- 87. Absorption and emission of light.- 88. Emission and absorption coefficients.- 89. The correspondence principle.- 90. Selection rules for dipole radiation.- 91. Intensities in the emission spectrum.- 92. Dispersion.- 93. Raman scattering.- 94. Allowance for change of phase of the electromagnetic field of the wave within the atom. Quadrupole radiation.- 95. The photoelectric effect.- XVI. The Passage of Microparticles Through Potential Barriers.- 96. Statement of the problem and simplest cases.- 97. The apparent paradox of the 'tunnel effect'.- 98. Cold emission of electrons from a metal.- 99. A three-dimensional potential barrier. Quasistationary states.- 100. The theory of a decay.- 101. Ionisation of atoms in strong electric fields.- XVII. The Many-Body Problem.- 102. General remarks on the many-body problem.- 103. The law of conservation of the total momentum of a system of microparticles.- 104. Motion of the centre of mass of a system of microparticles.- 105. The law of conservation of the angular momentum of a system of microparticles.- 106. Eigenfunctions of the angular momentum operator of the system. Clebsch-Gordan coefficients.- 107. The relation of the conservation laws to the symmetry of space and time.- XVIII. Simple Applications of the Theory of Motion of Many Bodies.- 108. Allowance for the motion of the nucleus in an atom.- 109. A system of microparticles executing small oscillations.- 110. Motion of an atom in an external field.- 111. Determination of the energy of stationary states of atoms from their deflection in an external field.- 112. Inelastic collisions between electrons and atoms. Determination of the energy of the stationary states of atoms by the collision method.- 113. The law of conservation of energy and the special significance of time in quantum mechanics.- XIX. Systems of Identical Microparticles.- 114. The identity of microparticles.- 115. Symmetric and antisymmetric states.- 116. Bose particles and Fermi particles. The Pauli principle.- 117. Wave functions for a system of fermions and bosons.- XX. Second Quantisation and Quantum Statistics.- 118. Second quantisation.- 119. The theory of quantum transitions and the second-quantisation method.- 120. The collision hypothesis. A Fermi-Dirac gas and a Bose-Einstein gas.- XXI. Multi-Electron Atoms.- 121. The helium atom.- 122. Approximate quantitative theory of the helium atom.- 123. The exchange energy.- 124. Quantum mechanics of the atom and Mendeleev's periodic system of the elements.- XXII. Formation of Molecules.- 125. The hydrogen molecule.- 126. The nature of chemical forces.- 127. Dispersion forces between molecules.- 128. Nuclear spin in diatomic molecules.- XXIII. Magnetic Phenomena.- 129. Paramagnetism and diamagnetism of atoms.- 130. Ferromagnetism.- XXIV. The Atomic Nucleus.- 131. Nuclear forces. Isotopic spin.- 132. Systematics of states of a system of nucleons.- 133. Theory of the deuteron.- 134. Scattering of nucleons.- 135. Polarisation in the scattering of particles which have spin.- 136. The application of quantum mechanics to the systematics of elementary particles.- XXV. Conclusion.- 137. The formalism of quantum mechanics.- 138. The limits of applicability of quantum mechanics.- 139. Some epistemological problems.- Appendices.- I. The Fourier transformation.- II. Eigenfunctions when there is degeneracy.- III. Orthogonality and normalisation of eigenfunctions of the continuous spectrum. The ?-function.- IV. The significance of commutability of operators.- VI. Hamilton's equations.- VII. Schrödinger's equation and the equations of motion in curvilinear co-ordinates.- VIII. Conditions on the wave function.- IX. The solution of the oscillator equation.- X. An electron in a uniform magnetic field.- XI. Jacobi co-ordinates.- References.