Introductory Quantum Mechanics

Introductory Quantum Mechanics
	Half-Title
	Prentice-Hall Physics Series
	Title-Page
	Copyright
	Preface
	Contents
I Mathematical Preliminaries
	1. Introduction
	2. Differential Operators
	3 The Operator minus d-square over dx-square
	4 The Operator minus d-square over dx-square plus x-square
	5 The Operator minus-i times derivative operator, x and c
	6. Simultaneous Eigenfunctions
	7. Degenerate Eigenvalues
	8. Orthogonal Sets of Functions
II Remarks On Classical Mechanics
	9. Hamiltonian Functions
	10. Examples of Classical Motion
	11. Distribution Functions
	12. Probability Packets
III Elements Of The Schroedinger Method; One Dimension
	13. Two Assumptions
	14. Schroedinger Operators
	15. Energy Levels of an Oscillator
	16. Schroedinger Functions
	17. Specification of States
	18. Energy States of an Oscillator
	19. Composition of States
	20. Resolution of States
	21. Probability Packets
	22. Coherent and Incoherent Superpositions of States
	23. Heisenberg Inequalities
	24. The Heisenberg Principle
	25. Kennard Packets
	26. Summary
IV Further Problems In The Schroedinger Method
	27. Linear Momentum
	28. The Free Particle in One Dimension
	29. One-Dimensional Rectangular Potential Wells
	30. The One-Dimensional Box
	31. Radiative Transitions
	32. Properties of the One-Dimensional First Schroedinger Equation
V Approximate Methods For Treating The One-Dimensional Schroedinger Equation
	33. Numerical Approximations
	34. Expansions in Powers of h
	35. A Variation Method
	36. A Perturbation Method for Nondegenerate States
VI One-Dimensional Probability Currents And De Broglie Waves
	37. Probability Current
	38. One-Dimensional Potential Barriers
	39. Virtual Binding
	40. Waves
	41. De Broglie Waves
	42. A Vibrating String and a Particle in a Box
VII Constants Of Motion
	43. Time Derivatives of Averages of Dynamical Variables
	44. Time Derivatives of Dynamical Variables
	45. Constants of Motion
	46. Dirac's Expansion Theorem
	47. Dynamical Variables Having no Classical Analogues
	48. Constants of Motion Having no Classical Analogues
	49. Potential Lattices and Energy Bands
VIII Remarks On The Momentum Method
	50. The Framework of the Momentum Method
	51. Energy Levels of an Oscillator
	52. Concluding Remarks
IX Linear Operators And Matrices
	53. Mappings of a Plane
	54. Representation of Mappings by Means of Matrices
	55. Different Coordinate Frames May Yield Different Representatives for a Given Operator
	56. Matrices and Vectors
	57. N-Dimensional Spaces
	58. Further Remarks on Matrices
	59. Function Space
	60. Representation of Differential Operators by Means of Matrices
	61. Concluding Remarks
X Elements Of The Heisenberg Method
	62. Heisenberg Matrices
	63. Heisenberg Matrices (Continued)
	64. The Heisenberg Method
	65. Energy Levels of an Oscillator
	66. Diagonalization of Matrices
	67. Approximate Diagonalization of Matrices
	68. The Matrix Perturbation Method for Nondegenerate States
	69. More Matrix Algebra
	70. The Heisenberg Representation of States
XI Remarks On The Symbolic Method
	71. Symbolic Operators and Operands
	72. Energy Levels of an Oscillator
	73. The Symbolic phi's
XII Problems In Three-Dimensional Motion; The Schroedinger Method
	74. Mathematical Preliminaries
	75. Remarks on Classical Mechanics
	76. Elements of the Schroedinger Method
	77. Elements of the Schroedinger Method (Continued)
	78. Central Fields
	79. The Free Particle; Polar Quantization
	80. The Bohr Formula for the Hydrogen Atom; Fixed Nucleus
	81. The Bohr Formula for the Hydrogen Atom; Free Nucleus
	82. The Fine Structure of the Hydrogen Levels
	83. Relativity Corrections for Hydrogen
XIII Elements Of Pauli's Theory Of Electron Spin
	84. The Electron-Spin Hypothesis
	85. Possible Values of Components of Angular Momenta
	86. The Pauli Operators and Operands
	87. The Simultaneous Eigen-psi's of J-z, L-square, and J-square
	88. Spin-Orbit Interaction and the Spin Correction
	89. The Spin-and-Relativity Correction for Hydrogen
	90. Space Functions and Spin Functions
XIV Elements Of Dirac's Theory Of The Electron
	91. The Dirac Equation for an Electron in an Electrostatic Field
	92. The Dirac gamma's
	93. The Existence of a 'Spin' Angular Momentum
	94. Constants of Motion for a Central Field
	95. The Radial Equations
	96. The Energy Levels of the Hydrogen Atom.
	97. The Normal State of the Hydrogen Atom
Appendix
	A few formulas involving Legendre functions and spherical harmonics
Index
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