Index

Abstract object, 161,279,284 concept of, 5, 6, 10 definition 8, 9 degree of abstractness, 9 denotation, 6, 9 least, 9 most, 9 name, 9 properties, 9 state of, 66, 78, 79 transition from more to less, 9

Abstract objects, equivalent, 24 set of, 21, 22 set of least, 34, 284

Accidental result, 16, 18, 19, 39 Action, 292,293 Action-at-a-distance, 323, 326, 329, 331 Activated complex, 244 Addition, 83

operation of, 83, 105 Adequate set, 23, 24, 144, 145, 161

choice verification, 30, 39, 67, 68, 70, 71,162

definition, 24, 25 general method of construction, 28

Ammonia inversion, 263, 362 Angular momentum, 172, 173, 205, 208,

209,304 component, 205 conservation law for, 172, 173, 210 intrinsic, 219, 220 magnitude, 173, 210, 215 maximum component, 173,210,215 operator for, 211 orbital, see angular momentum peculiarities of, 172, 173, 205, 209-

211,215,327 total,304

vibrational, 352 Angular velocity, instantaneous, 209 Arrhenius formula, 262 Atomic displacements, 350, 353 Auxiliary equation, 296, 297, 301-303,

305,333 Auxiliary function, 148, 154 Auxiliary operator, 301 Auxiliary quantity, 63, 64, 82, 83, 100,

115,130,138,220,272,317 Auxiliary variable, see auxiliary quantity Average value, 11, 58

statistical, 5 7 Avogadro constant, see Avogadro number Avogadro number, 181, 192

Basis, orthogonal, 95 orthonormal, 95, 97

Basis vector, 84 Bell,326 Bell's inequalities, 326, 329, 331 Ben's theorem, 326,327,329-331 Bernoulli's law, 44 Bernoulli's scheme, 41, 42,61,281 Bernoulli's theorem, 44, 281 Bertrand, 285 Bertrand's paradox, 30, 285 Bertrand's problem, 29, 30, 39, 73-76,

285-287 Black hole, 362 Bohm,326 Bohm's Gedankenexperiment, 327-331 Bohr uncertainty principle, 310 Boltzmann's constant, 71, 181, 184 Boltzmann's law, 71 Born-Oppenheimer approximation, 323,

346 b-representation, 128-130

363

364

Buffon,39 Buffon problem, 30, 38, 39

Canonical transformation, 292 Causal conditionality, 243 Causality, 277 Causality principle, 243, 244, 277 Certainty, 76 Chance concrete system, 325, 327 Characteristic function, 62, 63

properties of, 62, 63, 82, 83, 100, 161 Chemical process, see chemical reaction Chemical reaction, 243

absolute rate theory of, 244 Chicken-egg problem, 10, 11 Chords, set of concrete, 23, 25

sets adequate to, 25, 26, 29 Class, 7, 8, 143,145

defmition, 7 Class image, 8 Class measure, 13 Classes

relations between, 7, 8 set of, 7 union of, 8, 9, 21

Classical approach, 135, 161, see also Classical method.

Classical case, 223, 241 Classical limit, 135-137, 197, 223, 224,

231, 232, 236, 240, 241, 291, 322

Classical method, 162, 197,228, 233,236, 240

Classical system, 162 Clock, 266-268 Closed system, 166, 331

concrete, 162, 166, 277, 331 Closedness interval, 167, 170, 237, 238 Close-range-interaction, 323 Coin, good, 23 Commutator, 142, 342 Complete ph!\se space, see CPS Complex of conditions, 30, 320 Compton effect, 274 Concrete object, 3, 161, 279, 280

concept of, 3,4,10 continuous, 142,265 set of properties, 4, 22

Concrete objects, class of, 7-9 common property of 5 frequency of revelation of, 22 image of, 7, 9 manifold of sets of, 40

Index

mutual statistical adequacy of, 22 mutually adequate sets of, see adequate

sets properties of, 3,4, 142 relative measures of subsets of, 21 separate, 18 set of, 5-7, 21, 279, 280

division into classes, 7, 8 initial, 9, 22 measure of, 13, 22

set of all classes of, 9 set of all values of all properties of, 9 structure of set of, 17, 22

Concrete objects and abstract objects, rela-tionship between, 10, 11

Concreteness of experiment principle, 266 Condon, 303 Confidence, 76

degree of, 19, 76 practical, 76

Confidence interval, 76 Configuration,162,163

equilibrium, 255, 346 specific, 244

Configuration space, 162 Conservation law, 171, 173, 215, 223,

243,305,306,331 Conservative system, 162-164, 221, 222

abstract, 223 concrete, 162, 163

Continuous concrete objects, set of, 143, 144

Coordinate, 161 operator for, 199, 200

Coordinates Cartesian, 351 internal, 205, 245, 257, 258, 346, 350,

351,353 Coordinate system, inertial, see ICS

initial rest, see laboratory system rotating, 205, 208, 209, 346, 348

Corpuscular properties, 271, 318 CPS, 164,166-168 CP-trajectory, 164, 166-168 Coulomb field, 303, 304 C-trajectory, 162, 163

De Broglie relation, 271 Decay,244,248,249,253,254,274 Decay law, 253, 307

exponential, 254, 307 nonexponential, 254, 307 real, 254

Index

Decay probability per unit time, 253 Decay process, see decay Decay rate constant, 307, 309 Decay theory, conventional, 306, 307 Deformation, 143 Degree of confidence, 19 Degrees of freedom, number of, 192 Del operator, 202 Density matrix, 238, 239 Density operator, 83, 100, 101, 104-106,

130,161,239,240 Derivative of r(A) with respect to A, 126 Diffraction experiment, 68-70 Diffraction method, 272 Diffraction ofpartic1es, 68,318 Diffraction pattern, 68, 69,318, 319 Drrac, 295, 298, 299 Drrac equation, 296, 297, 301, 305, 332,

333 Drrac delta-function, 50, 54, 85 Drrac matrices, 297, 301 Drrac notation, 312 Drrac operator, 297 Drrect product, 298 Dispersion formula, 307 Distribution, 11, 12

binomial, 42 canonical, 181, 189, 196 equilibrium, 189 function, 49,50,82,161

joint, 52, 121 micro canonical, 175, 196,197,224,

233 normal, 254

Doppler effect, 274, 275 I>-function, 51, 64, 81, 82, 109, 111, 225,

228 I> l!2-function, 106, 111, 112

Eckart conditions, 353 Eigenfunction, 131

common, 215 Eigenvalue, 88

degenerate, 88 Eigenvalues, set of, 215 Eigenvector, 88 Einstein velocity summation, 275 Electromagnetic field, 265, 266, 270,

274,301 formal quantization of, 265

Electromagnetic wave, 265, 271 Electron, abstract, 296, 301, 305

concrete, 221

Electronic state, 256 ground, 256

Electrostatic field, 323 Elementary events, 33, 284

set of, 33, 34, 284 union of, 38

Elementary particles, 248 Emon, 272, 274, 323

abstract, 274 concrete, 272, 273, 275 rest mass of, 272, 273 velocity, 272, 273

Energy, 164, 263, 270, 271 conservation law for, 171-173, 223 electronic, 323 emonic,323

365

Energy levels, negative, see energy values, negative

operator for, 201, 294, 295 Energy values, complex, 307

negative, 297, 298, 302, 333 Ensemble method, 161, 168 Entropy, 185-189, 192, 193, 195

probabilistic definition of, 187 Entropy of mixing, 288 EPR,324 EPR paradox, 324 EPR thought experiment, 324, 326 Equilibrium, 176

thermal, 256, 261, 263 Equivalent elements, 24 e-representation, 89, 94, 95, 107 Ergodic hypothesis, 197 Estimate, 76 Euler's angles 205, 208, 210, 346 Event, 30, 266, 280, 320

abstract, 48,281,282 certain, 34 concrete, 48, 281, 283 frequency of appearance, 48 rrnpossible, 34 opposite, 34

Events, difference of, 34 incompatible, 34, 106 independent, 38 intersection of, see Events, product of product of, 33 set of concrete, 283 sum of, 33, 106 union of, see Events, sum of

Expansion, coefficients of, 84 spectral, 90, 94

Expansion of unity, 90,94

366

Exponential law, 247, 248 ,,-derivative, 81

sequence of, 81, 109-111 e-differentiation, 81, 107, 110, 111

Field, 142, 143 central, 232 gravitational, 324

Field energy, 265 Force, 162, 219

operator for, 219 time-independent, 162

Force coefficients, matrix of, 258 Formal quantization, 265 Four-momentum, 268-270 Four-quantity, 269, 270 Four-vector, 266, 267, 269

magnitude squared of, 267 Four-velocity, 267, 269 Fourier method, 151, 152, 154, 156 Fourier transfonn, 62, 63 Free energy, Helmholtz's, 185, 188, 195,

288-290 Free particle, 64, 268, 269

nonrelativistic, 224, 227 relativistic, 227, 228,296-298

Frequency, 19, 22,265,271,272,280 circular,258,265 radio wave, 273

lower limit of, 273 statistical, 19 vibrational, 258

Frobenius relation, 350 Function as a matrix, 85 Function ofinteger, 84 Function space, 85, 92, 95, see also Func>-

tional space Functional, 146-151, 188 Functional derivative, 146-150 Functional space, 133, 311 Functions, canonically conjugate, 148, 154

Gamovtheory, 307 Gamov complex energy eigenvalues, 307,

308 Gamov decay constant, 307 Gas pressure, 71 Gedankenexperiment, see Thought ex­

periment Generalized coordinates, 163, 202, 209 Generalized function, see Dirac delta­

function Generalized momenta, 163, 202, 209

Index

Gibbs, 161 Gibbs' distribution, see Distribution, micro­

canonical Gibbs ensemble method, see ensemble

method Gibbs paradox, 288-290 Gravon,324

Hamilton function, 292, see also Hamiltonian function

Hamiltonian general rotation-vibration, 203, 353 kinetic part of, 204, 346 operator for, 201, 346

Hamiltonian questions, 115, 118, 119, 145, 149, 154

generalized, 118 parametric, 116

Hamiltonian function, 115, 117,119,120, 148, 149, 163, see also Hamilton function

parametric, 116, 149 Hamiltonian partial equation, 149, 157 Hamiltonian random variables, 121-123,

133-136,154,197,198 probability distribution for function of,

121,122 Hamilton-Jacobi equation, 292-294 Hannonic approximation, 257, 258 Harmonic oscillator, linear, 197, 232, 257,

258 HCPS, 164, 166 Heat, 185 Heisenberg uncertainty principle, 314 Hermite polynomials, 134 Hennitian operator, 96, 101, 107, 125,

133 definition domain of, 106-108 spectrum of, 135, 198, 284

Hermiticity, see Operator, hermiticity of Heviside function, 81 Hidden variables, 321

ICS,243,266,268-271,274 Ideal gas, 193, 194, 288, 289

monoatomic, 177, 240 pressure, 184-186, 194

partial, 194 state equation of, 184

Identical particles, 290, 291 indistinguishability of, 290, 291 set of, 332

Identity, 353

Index

Imaginary experiment, see thought ex-periment

Initial conditions, 164-168 Interaction, 243, 244 Interatomic distances, 346 Internal energy, 185, 190, 192, 194

translational part of, 194, 195 Intramolecular rearrangement, 244, 255-

257,262 rate constant estimate of, 261-263

Intramolecular vibrations, 256

Joint distribution function, 52 Joint mathematical expectation, 124 Joint probability, 316, 317 Joint probability density, 52,53,122-124,

174,316,317 for function of random variables, 53,54

Joint probability distribution, 52, 123, 130, 136,247,315,316

Key methodological principle, 10, 11, 247 Kinetic energy, 163, 201, 204

operator for, 201, 204 rotational, 207, 208

Klein-Gordon equation, 297 Kolmogorovaxioms, 282-284 Kroneker delta, 85 Kroneker product, 298 Kroneker symbol, continuous, 226

Laboratory system, 205 Lagrange function, see Lagrangian function Lagrangian equations, 114, 118, 119, 145,

151-154,163 Lagrangian function, 114, 119, 120, 147,

151,152,163 parametric, 115

Lagrangian partial equation, 148, 151, 152, 157

Laguerre polynomials, 236 Landau, 295 Law

Bernoulli's, 281 binomial, 42, 45 normal, 45, 61 Poisson's, 45, 46

Law oflarge numbers, 44,281,282 Bernoulli's, see Bernoulli's theorem

Lebesgue measure, see Measure (L) Legendre polynomials, 218, 236 Light in vacuum, velocity of, 266, 272 Lifshitz, 295

Limiting process, 269 Liouville's equation, 197 Local realistic theory, 326, 328, 331 Locality, 328 Lorentz transformation, 266, 267

Magnetic moment, intrinsic, 304 Mandelstam, 295 Margenau, 311 Mass, 268, 271

367

Mathematical expectation, 57, 100, 101, 132, 136, 137, 182, 187, 198, 221,226,227,238,328,329

definition of, 57 of constant, 58, 102 of product, 59,102,103 of sum, 58, 102

Mathematical statistics, 67 Matrices

product of, 84, 87, 146 similarity of, 88 sum of, 84 transposition of, 84, 91

Matrices of infinite dimension, 92 Matrix, 87

adjoint, 107 column, 84 components of, 89, 90

expansion in terms of, 89 diagonal, 89 Hermitian, 94 inverse, 88 row, 84 trace of, 92 transposed, 91 unit, 84,88 unitary, 96

Matrix calculus, 84 Matrix representation, 108 Matrix transposition, 91 Matter, 171 Maxwell equations, 265 Maxwell (-Boltzmann) velocity distribution,

183 Mean-square amplitude, 261 Measure (L), 12-14, 23

approximate, 15, 16 experimental, 15, 16 necessary conditions for introduction of,

23 properties of, 13 relative, 15, 16, 279, 280

Measure theory, 282

368

Measurement, 312, 313, 325-327 concrete, 313 separate, see Measurement, single simultaneous, 314-317 single, 279, 314

Mechanical system, 162, 163, 198 abstract, 198, 211 concrete, 143 motion of, 162, 163 state of, 78

Mental experiment, see Thought experiment Microobject, see Microsystem Microsystem, 162 Molecular vibrations, see Intramolecular

vibrations Molecule, diatomic, 350

linear, 346, 349 single, 175, 255 undistorted, 346 vibrations of, 256

Moment, 59 central,59 initial,59 order of, 59

Moment of inertia matrix, instantaneous, 207

Momentum, 69, 70, 208 conservation law for, 171-173 operator for, 199, 200

Most probable value of m, 42, 43 Motion

condition of reality, 164 free, 243 real, 162, 163, 221, 266, 267

ultimate velocity of, 263 reality of, 321, 324 rotational, see Rotation translational, 194

Multiplication, 83 Mutually adequate sets, 27, 28

Nabla operator, see Del operator Natural phenomena, 18, 69 Neutrino, 266 Nonclosed system, 165 Nonconservative system, 162, 165 Normal coordinates, 257, 258 Normal vibrations, 156

modes of, 156 Normalization constant, 123 Normalization factor, see Normalization

constant Normalization to delta-function, 101

Index

Normalization to unity, 102 Nuclear reaction, 243 Null cone, 267-269

vertex of, 268 Numerical experiment, 73

Observable, 312, 313, 318 One-dimensional motion, model of, 244,

245,257 Operator, 85

adjoint, 95 defmition domain of, 86 derivative of, 124, 125 domain of values, 86 e-differentiation, 107 function of, 90, 96 Hamiltonian, see Hamiltonian Hermitian, see Hermitian operator hermiticity domain of, see Operator,

hermiticity range of hermiticity of, 108, 311, 312 hermiticity range of, 138-140, 200,

311,312 identical transformation, see Operator

unit identity, see Operator unit inverse, 87 kernel of, 92, 98-100,111 linear, 85, 125 multiplication by number, 85 multiplication by operator, 86, 87 partial derivative of, 125, 126 polynomial differential, 146 projection, 90,91,97-99,101

expansion in terms of, 90, 101 kemelof,94

self-adjoint, 96 spectrum of, 101 trace of, 92, 97-99, 108-109 transposed, 91, 94 unit, 86, 125 unitary, 96

Operator of differentiation, 107, 109, 126, 127

Operator of multiplication, 109, 125, 127, 140, 199

Operators canonically conjugate, 124, 125, 131,

337-345 independent pairs of, 127, 128, 344,

345 derivative of their function, 129

commutative, 97

Index

commutativity of, 315-318 equal,85 noncommutative, 103 product of, 86, 96 similar, 88, 92 simultaneously reducible, 97 sum of, 85, 96 symmetrized product of, 104

Ordinal number,S, 84 O-vector,84

Paradox, 10, 11, 312 chicken-egg, 10, 11

Particle abstract, 266, 319 charged, 301

relativistic, 302 classical, 318 concrete, 166, 266, 269, 270 nonrelativistic, 224 spin %,297,299,326

Particles, set of concrete, 266 Particle path, 162, 163 Partition function, 181,182,195,288-290

translational, 195, 196 Path

concrete, 318, 321 definite, 321

Pauli, 295 Pauli exclusion principle, 333 Pauli matrices, 221, 297, 300, 301 Pauli theory, 305 Peieris, 312 Pendulum, harmonic, 79

state of, 79 Phase space, 163, 164 Phase velocity, 273 Photon,265,266,270,271

abstract, 271, 272 concrete, 265, 275 separate, 271, 272

Photons absorption of, 243, 272 emission of, 243, 253, 274

Photoelectric effect, 274 Physical property, see Physical quantity Physical quantities, conserved in common,

173 Physical quantity, 161, 198, 313

conserved, 173,255 derivative of, 219

operator for, 219 operator for, 213, 219

Physical space, 162, 163 homogenity of, 171, 172 isotropy of, 171, 172

Physical system, 161

369

abstract, 161, 168, 173, 198, 277,314 concrete, 161,243,277,313,314 concrete macroscopic, 190

microstructure of, 190, 191, 289 macroscopic, 192, 215 microscopic, 215, see also Microsystem state of, 78

Physical systems, classification of, 162 Physically different situations, 244 Planck constant, 196, 199 Poisson bracket, 117, 150

expanded, 116, 117,150 Population, 75

census, 66 interviewing of, 18,66

Positron, 301 Positron-electron annihilation, 243 Potential barrier, 249, 257

penetration through, 322 square-topped, 250

Potential energy, 163, 323 electrostatic, 323 operator for, 201

Potential field, see Potential energy Potential well, 249, 257

harmonic, 257 Probabilistic approach, see Probabilistic

treatment Probabilistic consideration, see Probabilistic

treatment Probabilistic meaning, 63, 64, 100, 185,

187,196,239,311 Probabilistic mechanics, 174 Probabilistic physics, 10, 67, 161, 173, 198,

277, 313, 314, 318, 326, 327, 331

Probabilistic problem, 22, 29, 121, 136, 168, 170, 171, 197, 283

statement of, 23 Probabilistic statement, 168, 314 Probabilistic treatment, 130, 145, 161,

196, 198, 265, 329 Probabilistics, 10, 21, 22, 76, 78,130,143,

161, 197, 265, 277, 279, 283, 318

basic phenomenon of, 279, 280, 282, 284

principal premises of, 16, 27 Probabilistics concrete object, 280-282

370

Probabilities addition theorem, 35, 36, 105, 106, 319,

320 measurement of, 22 multiplication theorem, 37 properties of, 21, 36 single measurement of, 22, 280

Probability, 10, 19, 21, 246,280 existence of, 28 general definition of, 25-27 geometrical, 30, 39, 287 measured value of, 22 preliminary defmition of, 19-22 sta tistical, 19

manifestation of, 22 Probability density, 26, 49-52, 82, 100,

102,161,239,246 approximate, 51, 52 conditional, 37, 239, 246, 284

Probability distribution, 36, 49, 121, 136, 161,221, 319

approximate, 50, 51 characteristics of, 70, 71 classical statistical, 162 conditional, 238 experimental determination of, 70 function, see Distribution function

Probability distributions, mutually inde­pendent, 52, 63, 316

Probability problem, see Probabilistic problem

Probability theory, 44, 67, 279 axiomatic, see Probability theory,

ordinary conventional, see Probability theory,

ordinary customary, see Probability theory,

ordinary Kolmogorov's, see Probability theory,

ordinary ordinary, 21, 30, 277, 282, 283

incompleteness of, 21, 283 Process, 243, 244

concrete, 243, 277 internal, 243 many-stage, 249 nonstationary, 256 one-step, 249, 253,254,262 reversible, 186 stationary, 256 two-step, 262

Process path coordinate, see Transformation path coordinate

Products, quality of, 69, 70 Proper time, 267 Properties, probabilistic, 271

set of, 4,22 Property 4

combined, 4, 7 values of, 3, 4

Index

Pseudoclosed subsystem, 165, 237, 238, 249

Pseudoc1osed system, 165-167, 170, 171, 196

separate, 176

Quality-control device, 96, 70 Quantities, canonically conjugate, 151, 163 Quantization, 265 Quantum, 165 Quantum approach, 133-136, 156, 157,

161, 162, 195, 197, 198, 229, 235, 236, 265

peculiarities of, 133-135 Quantum case, 211, 223, 241 Quantum equation, 157 Quantum mechanics, 162, 197, 198,318

causality in, 277 principal propositions of, 198

Quantum number, 135, 136, 224, 232, 236, 241,261

summed, 259 rotational, 256 vibrational, 258

Quantum physics, 10, 100, 221, 277 Quantum theory, see Quantum physics

Random constant, 48 Random event, see Event Random experiment, 23 Random field, 143-145, 155, 265, 266

auxiliary, 155 Hamiltonian, 154-157, 265 k-dimensional, 143 one-dimenmonal, 143

Random fields, set of, 143 Random function, 143, 144

Hamiltonian, 154-156 k-dimensional, 143 one-dimenmonal, 143

Random functions, set of, 143 Random numbers, 72, 74, 75

criterion for correctness, 72, 73 sequence of, 72 set of, 72, 73

Random path, concrete, 321

Index

Random sample, 75, 76 Random sampling, 17, 18 Random test, 16, 17, 19, 20, 22, 144,145,

280 single, 23, 30, 39,40

Random tests, separate, 67 sequence of, 40 set of, 22

Random trajectory, concrete, see Random path, concrete

Random variable, 47,161,244,318 auxiliary, 156, 157 continuous, 48 definition of, 47, 48, 284 discrete, 48 first-type, 144, 145, 154-156 k-dimensional, 47, 48, 52 mixed type, 48 multidimensional, see Random variable,

k-dimensional second-type, 145, 154-156 unidimensional, 47,48

Random variables canonically conjugate, 122, 138, 156

operators for, 101-104, 106, 130-133,137, 138, 162, 331

functions of, 47 probability density of, 53, 54

functional dependence of, 56 Hamiltonian, see Hamiltonian random

variables product of, 103 quantization of, 106, 133, 134 quantized values of, 106 values of, 48

Random vector, k-dimensional, see Random variable, k-dimensional

Randomness, 16-18, 144, 176, 280, 281, 310,326

Rate, 249, 262 conditional average, 249 mean, 248, 262

Rate constant, 247-249, 251, 255, 256, 258

Reaction volume, 255 Realistic theory, see Local realistic theory Relative stability interval, 252-254, 309

width of, 252, 253 Relativistic aberration, 274, 275 Relativistic theory, see Special relativity Representation, 88, 90

coordinate, 199 Representation space, 88

Rest mass, 266, 267, 269, 272, 273 nonzero, 268, 272 zero, 265, 266, 268,270

Rotation, 156, 256 Rotational state, 256

Sample, see Random sample volume, 76

Scalar, 267 Scalar product, 94, 95, 128, 146, 311

incomplete, 128, 129

371

Schri.idinger cat, 64, 112, 357, 358 Schri.idinger equation, 221, 222, 224, 237,

292-295,332, 333 relativistic, 297 without time, 222, 227, 229, 235, 250,

253, 257 Schri.idinger wave equation, see Schri.idinger

equation Schwartz's inequality, 94, 95, 139 Science of probability, see Probabilistics Second quantization, 332, 333 Sequence of independent tests, 41 Set

complement of, 8, 34 empty, 8 finite, 4 measurable (L), 13 measure (L) of, 12-14 nonenumerable, 4 subset of, 7, 8 zero-measure, 14

Set of values, 4 Sets, difference of, 8

direct product of, 4 measure of, 41

equivalent, 24 identical, 19, 24 intersection of, 8 nonintersecting, 8 union of, 8

Shortley, 303 Similarity transformation, 88, 89, 353 Slater, 263 Space, 266

dimension of, 92 e-representation, 84, 88 finite-dimensional, 108 four-dimensional, 268 infinite-dimensional, 108

Spaces, direct product of, 103 Space basis, 84, 89 Space-time, 266, 267, 318

372

Specialrelativity, 265, 266, 270, 274 Special relativity theory, see Special relativity Specific state, 328 Specific volume, 185 Spectrum

continuous, 102, 250 discrete, 102

Spherical functions, 218 Spin,219,220,241,304,305

magnitude squared, 220 peculiarities of, 219, 220, 330

Spin component, 327 Spin function, 327 Spin particle, concrete, 327, 331 Spin state, 326 Stabilization, 261 Standard deviation, 138, 192, 271, 310,

315 Standard deviations, universal inequality

for, 139 State, 66, 78, 156, 157, 161

description of, 79, 80, 82, 100, 104, 105, 111, 112, 131, 132, 161, 198

approximate, 81, 82, 106 deterministic, 328, 330 equation of, 184, 185 equilibrium, 181 nonstationary, 223, 309 real, 215, 221, 303 rotational, 256 vibrational, 258, 261

State function, 221 State vector, 83, 100-102, 104-106,

130,161,284 expansion of, 102

Stationary state, 222-224, 257, 309 Stationary states, set of, 251 Statistical adequacy, 22 Statistical average, 254 Statistica1data, 16, 19, 66, 314 Statistical distribUtion, 70, 176,272,319 Statistical experiment, 16-18, 67, 104,

122,157,162,175 Statistical material, see Statistical data Statistical meaning, see Probabilistic meaning Statistical measurement, 280,

single, 280-282 Statistical mechanics, 174, 182

classical, 174,182,240,277 quantum, 236

Statistical method, 16-19, 22, 67, 68, 70, 280,281

main condition of, 16 peculiarities of, 67, 68

Statistical physics, 67, 71, 187 classical, 161, 162 quantum, 240

Statistical results, see Statistical data stability of, 27, 28

Statistical tests, see Random tests Statistical weight, 191 Statistics, 44, 66, 67

Index

experimental, 16,44,66,67, 279, 282 general task of, 67, 76

Stirling formula, 42 Subsystem, 165 Surprises in theoretical physics, 312 System, big concrete, 190-192, see also

Physical system Systems, concrete, statistical density of, 254

separate, 1 75

Temperature, 185, 193 absolute, 71, 181, 193,240,259

Tensor product, 298 Tests, see Random tests

successive, 40 Thermodynamic function, 185, 196,241

additivity of, 289, 290 Thermodynamic property, see Thermo­

dynamic function Thermodynamic quantity, see Thermo-

dynamic function Thermodynamic relations, 71 Thermodynamic state, 185, 191 Thermodynamics, 181, 182, 185, 187 Thermostat, 176, 177, 179-182, 237, 240 Thought experiment, 175, 266, 314, 315,

327,328 Three-momentum, 268 Time, 161,163, 164

homogeneity of, 171, 172 irreversibility of, 277 operator for, 201, 295, 296

Total derivative, 147, 150 Transformation, 85, 244-247, 249, 258

one-step, see Process, one-step Transformation direction, 249, 263 Transformation path coordinate, 245, 249,

257,258 Transformation process, see Transformation Transformation product, 249 Transformation rate constant, see Rate

constant Transition state, 244

Index

Transitional configuration, 244, 245, 249, 250,253,256,257,259,261

principle of, 244, 245, 249, 253 theory, 249

Transitional interval, 245 Transitional point, 245 Translation, 156 Transposition, 84 t-representation, 102 Two-particle system, 325, 326 Two-slit experiment, 319-321

Ultimate velocity, 265, 266, 270, 272 Uncertainty relation

coordinate-momentum, 310, 311 general, 310 Heisenberg's 315 time-energy,310

Unitary transformation, 96,97

Value distribution, 11 Values

set of, 3-7, 142 union of all sets of, 9

Variables, canonically conjugate, 115, 118 Variance, 59,104,138 Variant, 245

abstract, 245-249, 261 concrete, 245

Variants, set of concrete, 245 Variational condition, 114, 147, 151, 188 Variational derivative, see Functional

derivative Vector, 83

expansion of, 84, 85, 98 multi-dimensional, 100

unidimensional, 100 unit, 95, 101

Vectors essentially different, 105 linear combination of, 88 linearly dependent, 83 linearly independent, 83 nonessentially different, 105 orthogonal, 95

Vector space, 83 Velocity, 228, 245, 246

measurement of, 273, 274 operator for, 219,227

Very-long waves, 274 von Mises, 281, 283

Wave, 318 Wave-corpuscle duality, 274, 318 Wave function, see State function Wavelength, 271, 272 Wave packet, 306 Wave properties, 271, 274, 318, 319 Wave spin function, see Spin function Weight function, 95, 199, 311 Weyl, 295 World line, 267-269 Work, 185

373

x-representation, 100, 101, 111, 125, 126, 132,133

xj-representation,131 xn+j-representation,131

Zero rest mass, see Rest mass, zero Zero state energy, 265 Zero vector, see O-vector