| Historical Introduction | p. 1 |
| Planck's theory of blackbody radiation | p. 1 |
| Einstein's photon theory of light | p. 7 |
| Bohr's theory of the hydrogen atom | p. 11 |
| Sommerfeld's generalization and the old quantum theory | p. 17 |
| De Broglie's wave theory of matter | p. 26 |
| The development of quantum mechanics | p. 30 |
| The Schrodinger Equation and Its Mathematical Implication | p. 35 |
| Relations between the law of mechanics of a particle and the law of wave propagation | p. 35 |
| The equation of motion of a wave packet | p. 42 |
| Mathematical formulation of quantum mechanics-the Schrodinger equation | p. 45 |
| The statistical interpretation of the Schrodinger equation | p. 48 |
| The uncertainty relation | p. 52 |
| Newton's second law of motion as a special case of quantum mechanics | p. 54 |
| Quantum mechanics and the Hamiltonian theory | p. 58 |
| Normalization. The probability current density | p. 62 |
| The general solution of the time-dependent Schrodinger equation | p. 65 |
| Summary | p. 68 |
| The Free Particle | p. 71 |
| The general solution in classical mechanics | p. 71 |
| The general solution in quantum mechanics | p. 71 |
| Classical mechanics as a special case of quantum mechanics | p. 73 |
| Explanation of a quantum phenomenon: the wave property of matter | p. 77 |
| The Linear Harmonic Oscillator | p. 81 |
| The general solution in classical mechanics | p. 81 |
| The general solution in quantum mechanics | p. 81 |
| Classical mechanics as a special case of quantum mechanics | p. 88 |
| Explanation of a quantum phenomenon: the quantization of energy | p. 95 |
| One-dimensional Potential Barrier Problems | p. 99 |
| The potential well problem | p. 99 |
| The potential barrier problem | p. 104 |
| Explanation of a quantum phenomenon: the penetration of potential barrier in radioactive decay | p. 108 |
| The Physical Meaning of Quantum Mechanics | p. 112 |
| Critiques of the classical concepts in mechanics. Heisenberg's uncertainty principle | p. 112 |
| Quantum-mechanical description of physical processes. The law of causality | p. 125 |
| Explanation of the quantum phenomena | p. 131 |
| The wave property of matter | p. 132 |
| The quantization of energy | p. 133 |
| The penetration of potential barrier | p. 134 |
| Concluding remarks | p. 136 |
| General Methods for One-dimensional Problems | p. 140 |
| Qualitative properties of the one-dimensional wave function | p. 140 |
| Approximate solution by the WKB method | p. 143 |
| Three-dimensional Problems | p. 150 |
| The space rotator | p. 150 |
| Central force problems | p. 157 |
| The hydrogen atom | p. 162 |
| The positronium, mesic atoms, ionized atoms, alkali atoms, and exciton | p. 175 |
| The Three-dimensional Harmonic Oscillator | p. 181 |
| Solution in rectangular coordinates | p. 181 |
| Solution in cylindrical coordinates | p. 184 |
| Solution in spherical coordinates | p. 190 |
| Orthogonality of the wave functions | p. 195 |
| Time-independent Perturbation Theory | p. 199 |
| Perturbation theory for nondegenerate levels | p. 199 |
| Perturbation theory for degenerate levels | p. 207 |
| A generalized perturbation theory | p. 213 |
| The Stark effect | p. 217 |
| The old quantum theory | p. 218 |
| The nondegenerate perturbation method | p. 220 |
| The degenerate perturbation method | p. 223 |
| The generalized perturbation method | p. 225 |
| Time-dependent Perturbation Theory | p. 231 |
| General theory of time-dependent perturbation | p. 231 |
| The sudden and the adiabatic approximations | p. 244 |
| Transition to continuous states | p. 256 |
| The Rutherford scattering | p. 267 |
| The classical theory | p. 268 |
| The time-dependent perturbation theory | p. 270 |
| The time-independent perturbation theory | p. 275 |
| The radiation processes | p. 280 |
| The perturbation treatment of the radiative transitions | p. 281 |
| Transition probabilities; selection, intensity, and polarization rules | p. 286 |
| The spontaneous emission | p. 293 |
| General Formulation of Quantum Mechanics and Its Applications | p. 297 |
| Dynamical quantities represented by operators | p. 297 |
| The algebra of operators | p. 306 |
| Angular momentum in quantum mechanics | p. 311 |
| Position eigenfunctions and the principle of superposition | p. 315 |
| Equations of motion in the operator form | p. 319 |
| General formulation of quantum mechanics | p. 322 |
| Classical mechanics as a limiting case of quantum mechanics | p. 332 |
| Quantization of many-particle systems | p. 334 |
| Quantization of the motion of a rigid body | p. 339 |
| The plane rotator | p. 339 |
| The rigid rotator | p. 341 |
| The symmetric top | p. 342 |
| Quantization of the motion of a charged particle in a magnetic field | p. 347 |
| Quantization of the radiation field | p. 352 |
| Quantization of the matter wave | p. 357 |
| Matrix Mechanics | p. 361 |
| Introduction | p. 362 |
| Matrix formulation as a substitute for classical mechanics | p. 363 |
| The commutator of momentum and coordinate | p. 365 |
| Table of Physical Constants | p. 369 |
| Index | p. 371 |
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