简介
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.
目录
Preface p. vii
Newtonian Dynamics p. 1
Introducing Probability p. 1
Solving Dynamics Problems p. 13
Initial conditions p. 14
Solving Liouville equation p. 20
Exact solution p. 20
Numerical solution p. 21
Perturbation solution p. 22
Analysis of final results p. 25
Simple Systems p. 27
Point-Like Density p. 27
Free Particle p. 28
Constant Force p. 29
Oscillator in the External Field p. 30
Friction Force p. 32
Step Potential p. 33
Central Force p. 41
Angular Momentum p. 51
General Remarks p. 51
Factorization of Phase Space Density p. 54
Internal Rotation p. 58
Rotating force p. 58
Electromagnetic force p. 61
Spin p. 63
Special Phase Space Densities p. 73
Stationary Phase Space Density p. 73
Infinite potential well p. 75
Finite potential well p. 80
Discrete Phase Space Densities p. 85
Phase Space Density with Constrains p. 90
Energy constraint p. 91
Angular momentum constrain p. 93
Interaction of Two Particles p. 97
Forces with Time Delay p. 97
Space-Time Unification p. 103
Uniform motion of source p. 105
Space-time transformation p. 108
Dynamics equations p. 112
Examples of Lorentz Invariant Dynamics p. 123
General Remarks p. 123
Free Particle p. 127
Constant Force p. 127
Harmonic Force p. 128
Kepler Problem p. 134
Lorentz Invariant Liouville Equation p. 141
General Theory p. 141
Free Particle p. 143
Scattering on Step Potential p. 149
Charge in the Electromagnetic Plane Wave p. 156
Scattering by Coulomb Force p. 161
Non-Uniform Motion p. 167
Euclidean Metric p. 169
Riemann Metric p. 176
Field and its Source p. 183
Delocalized Source p. 183
Energy in Field p. 188
Field Reaction Force p. 197
Implementation of Uncertainty Principle p. 207
Constraint on Phase Space Density p. 207
Probability Amplitude p. 215
General properties p. 215
Methods of Solution p. 228
Exact analytic methods p. 229
Perturbation methods p. 232
Numerical methods p. 235
Typical Solutions p. 239
Free Particle p. 239
Diffraction p. 242
Interference p. 248
Constant Force p. 256
Harmonic Force p. 259
One dimension p. 259
Three dimensions p. 264
Time Varying Constant Force p. 269
Rigid Rotor p. 273
Impulsive Force p. 281
Elastic Scattering p. 281
One dimension p. 281
Three dimensions p. 287
Inelastic Scattering p. 307
Laboratory Coordinate System p. 307
Particle-Harmonic Oscillator Collision p. 314
Particle-Rigid Rotor Collision p. 322
Scattering by Time Dependent Force p. 330
Dynamics in the Electromagnetic Field p. 337
Radiation by Charge p. 347
General Theory of Spectrum p. 347
Spontaneous Emission p. 352
Induced Emission p. 361
Collision induced emission p. 362
Time dependent force p. 366
Particle Manifestation of the Electromagnetic Field p. 377
Photoelectric Effect p. 377
Coincidence Effect p. 385
Photon p. 391
Spin p. 399
Free Particle p. 399
Interaction with the Electromagnetic Field p. 406
Lorentz Invariant Dynamics with Spin p. 409
Arbitrary Potential p. 421
Step Potential p. 421
Generalized Potential p. 429
Random Numbers p. 435
Basics of Differential Geometry p. 439
Spherical Coordinates p. 459
Bibliography p. 465
Index p. 467
Newtonian Dynamics p. 1
Introducing Probability p. 1
Solving Dynamics Problems p. 13
Initial conditions p. 14
Solving Liouville equation p. 20
Exact solution p. 20
Numerical solution p. 21
Perturbation solution p. 22
Analysis of final results p. 25
Simple Systems p. 27
Point-Like Density p. 27
Free Particle p. 28
Constant Force p. 29
Oscillator in the External Field p. 30
Friction Force p. 32
Step Potential p. 33
Central Force p. 41
Angular Momentum p. 51
General Remarks p. 51
Factorization of Phase Space Density p. 54
Internal Rotation p. 58
Rotating force p. 58
Electromagnetic force p. 61
Spin p. 63
Special Phase Space Densities p. 73
Stationary Phase Space Density p. 73
Infinite potential well p. 75
Finite potential well p. 80
Discrete Phase Space Densities p. 85
Phase Space Density with Constrains p. 90
Energy constraint p. 91
Angular momentum constrain p. 93
Interaction of Two Particles p. 97
Forces with Time Delay p. 97
Space-Time Unification p. 103
Uniform motion of source p. 105
Space-time transformation p. 108
Dynamics equations p. 112
Examples of Lorentz Invariant Dynamics p. 123
General Remarks p. 123
Free Particle p. 127
Constant Force p. 127
Harmonic Force p. 128
Kepler Problem p. 134
Lorentz Invariant Liouville Equation p. 141
General Theory p. 141
Free Particle p. 143
Scattering on Step Potential p. 149
Charge in the Electromagnetic Plane Wave p. 156
Scattering by Coulomb Force p. 161
Non-Uniform Motion p. 167
Euclidean Metric p. 169
Riemann Metric p. 176
Field and its Source p. 183
Delocalized Source p. 183
Energy in Field p. 188
Field Reaction Force p. 197
Implementation of Uncertainty Principle p. 207
Constraint on Phase Space Density p. 207
Probability Amplitude p. 215
General properties p. 215
Methods of Solution p. 228
Exact analytic methods p. 229
Perturbation methods p. 232
Numerical methods p. 235
Typical Solutions p. 239
Free Particle p. 239
Diffraction p. 242
Interference p. 248
Constant Force p. 256
Harmonic Force p. 259
One dimension p. 259
Three dimensions p. 264
Time Varying Constant Force p. 269
Rigid Rotor p. 273
Impulsive Force p. 281
Elastic Scattering p. 281
One dimension p. 281
Three dimensions p. 287
Inelastic Scattering p. 307
Laboratory Coordinate System p. 307
Particle-Harmonic Oscillator Collision p. 314
Particle-Rigid Rotor Collision p. 322
Scattering by Time Dependent Force p. 330
Dynamics in the Electromagnetic Field p. 337
Radiation by Charge p. 347
General Theory of Spectrum p. 347
Spontaneous Emission p. 352
Induced Emission p. 361
Collision induced emission p. 362
Time dependent force p. 366
Particle Manifestation of the Electromagnetic Field p. 377
Photoelectric Effect p. 377
Coincidence Effect p. 385
Photon p. 391
Spin p. 399
Free Particle p. 399
Interaction with the Electromagnetic Field p. 406
Lorentz Invariant Dynamics with Spin p. 409
Arbitrary Potential p. 421
Step Potential p. 421
Generalized Potential p. 429
Random Numbers p. 435
Basics of Differential Geometry p. 439
Spherical Coordinates p. 459
Bibliography p. 465
Index p. 467
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