Dynamics of particles and the electromagnetic field

Advances in experimental techniques allow investigating extremes of dynamics of particles in interaction with electromagnetic field. The theoretical tools at disposal are classical and quantum mechanics and the experience show that it is dangerous to dismiss one (classical) at the expense of the other (quantum): each one has merits that should be fully explored. The problem, however, is to bridge the gap between them so that the information they give is complementary and not contradictory. In the book this goal is achieved by formulating five postulates, and level of their implementation distinguishes the two mechanics. Dynamics of particles (charges) is not complete without unifying it with the dynamics of electromagnetic field, which in the book is given special emphases.

Preface	p. vii
1 Newtonian Dynamics	p. 1
1.1 Introducing Probability	p. 1
1.2 Solving Dynamics Problems	p. 13
1.2.1 Initial conditions	p. 14
1.2.2 Solving Liouville equation	p. 20
1.2.2.1 Exact solution	p. 20
1.2.2.2 Numerical solution	p. 21
1.2.2.3 Perturbation solution	p. 22
1.2.3 Analysis of final results	p. 25
2 Simple Systems	p. 27
2.1 Point-Like Density	p. 27
2.2 Free Particle	p. 28
2.3 Constant Force	p. 29
2.4 Oscillator in the External Field	p. 30
2.5 Friction Force	p. 32
2.6 Step Potential	p. 33
3 Central Force	p. 41
4 Angular Momentum	p. 51
4.1 General Remarks	p. 51
4.2 Factorization of Phase Space Density	p. 54
4.3 Internal Rotation	p. 58
4.3.1 Rotating force	p. 58
4.3.2 Electromagnetic force	p. 61
4.4 Spin	p. 63
5 Special Phase Space Densities	p. 73
5.1 Stationary Phase Space Density	p. 73
5.1.1 Infinite potential well	p. 75
5.1.2 Finite potential well	p. 80
5.2 Discrete Phase Space Densities	p. 85
5.3 Phase Space Density with Constrains	p. 90
5.3.1 Energy constraint	p. 91
5.3.2 Angular momentum constrain	p. 93
6 Interaction of Two Particles	p. 97
6.1 Forces with Time Delay	p. 97
6.2 Space-Time Unification	p. 103
6.2.1 Uniform motion of source	p. 105
6.2.2 Space-time transformation	p. 108
6.2.3 Dynamics equations	p. 112
7 Examples of Lorentz Invariant Dynamics	p. 123
7.1 General Remarks	p. 123
7.2 Free Particle	p. 127
7.3 Constant Force	p. 127
7.4 Harmonic Force	p. 128
7.5 Kepler Problem	p. 134
8 Lorentz Invariant Liouville Equation	p. 141
8.1 General Theory	p. 141
8.2 Free Particle	p. 143
8.3 Scattering on Step Potential	p. 149
8.4 Charge in the Electromagnetic Plane Wave	p. 156
8.5 Scattering by Coulomb Force	p. 161
9 Non-Uniform Motion	p. 167
9.1 Euclidean Metric	p. 169
9.2 Riemann Metric	p. 176
10 Field and its Source	p. 183
10.1 Delocalized Source	p. 183
10.2 Energy in Field	p. 188
10.3 Field Reaction Force	p. 197
11 Implementation of Uncertainty Principle	p. 207
11.1 Constraint on Phase Space Density	p. 207
11.2 Probability Amplitude	p. 215
11.2.1 General properties	p. 215
11.3 Methods of Solution	p. 228
11.3.1 Exact analytic methods	p. 229
11.3.2 Perturbation methods	p. 232
11.3.3 Numerical methods	p. 235
12 Typical Solutions	p. 239
12.1 Free Particle	p. 239
12.2 Diffraction	p. 242
12.3 Interference	p. 248
12.4 Constant Force	p. 256
12.5 Harmonic Force	p. 259
12.5.1 One dimension	p. 259
12.5.2 Three dimensions	p. 264
12.6 Time Varying Constant Force	p. 269
12.7 Rigid Rotor	p. 273
13 Impulsive Force	p. 281
13.1 Elastic Scattering	p. 281
13.1.1 One dimension	p. 281
13.1.2 Three dimensions	p. 287
14 Inelastic Scattering	p. 307
14.1 Laboratory Coordinate System	p. 307
14.2 Particle-Harmonic Oscillator Collision	p. 314
14.3 Particle-Rigid Rotor Collision	p. 322
14.4 Scattering by Time Dependent Force	p. 330
15 Dynamics in the Electromagnetic Field	p. 337
16 Radiation by Charge	p. 347
16.1 General Theory of Spectrum	p. 347
16.2 Spontaneous Emission	p. 352
16.3 Induced Emission	p. 361
16.3.1 Collision induced emission	p. 362
16.3.2 Time dependent force	p. 366
17 Particle Manifestation of the Electromagnetic Field	p. 377
17.1 Photoelectric Effect	p. 377
17.2 Coincidence Effect	p. 385
17.3 Photon	p. 391
18 Spin	p. 399
18.1 Free Particle	p. 399
18.2 Interaction with the Electromagnetic Field	p. 406
18.3 Lorentz Invariant Dynamics with Spin	p. 409
19 Arbitrary Potential	p. 421
19.1 Step Potential	p. 421
19.2 Generalized Potential	p. 429
Appendix A Random Numbers	p. 435
Appendix B Basics of Differential Geometry	p. 439
Appendix C Spherical Coordinates	p. 459
Bibliography	p. 465
Index	p. 467

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