Index. 3-j symbol, 415

Transcription

1 3-j symbol, 415 absorption spectrum, 22 absorptive power, 488 adjoint, 169 Airy function, 189 algebra, 76 alpha-rays, 160 analytic family of type (A), 281 angular momentum operators, 398 anharmonic oscillator, 252 annihilation operator, 379 Aristotelian setting, 50 asymptotic expansion, 174 asymptotic perturbation theory, 281 asymptotically free, 301 Auger states, 317 automorphism group, 168 automorphism of a Hilbert space, 168 azimuth quantum number, 163 Baker Campbell Hausdorff formula, 390 Balmer formula, 199 Bargmann Fock representation, 392 Barnes, Brascamp and Lieb, 268 beamsplitter, 410 Bell inequalities, 455 Berry phase, 466 Bessel equation, 224 function of first kind, 224 functions of second kind, 224 black body, 488 black-body radiation, 488 Bloch theorem, 219 Bohr magneton, 227 Bohr Sommerfeld conditions, 30 Borel transform, 282 Born approximation, 305 Born series, 306 Bose Einstein statistics, 508 boundary conditions, 147 bra, 172 Bragg reflection, 31 Breit Wigner resonance, 318 canonical commutation relations, 341 ensemble, 482 operators, 342 quantization, 343 transformation, 48 Cartan identity, 81 Casimir elements,

2 589 operators, 82 centre of an algebra, 77 characteristic function, 64, 458 chiral representation, 552 classical electron radius, 17 Clebsch Gordan coefficients, 413 closable operator, 169 closure, 169 coherent state, 389 compact operator, 170 compatible observables, 367 complete set of common eigenvectors, 367 completely canonical transformations, 54 Compton effect, 12 confluent hypergeometric equation, 198 confluent hypergeometric functions, 198 constant of motion in wave mechanics, 128 constants of motion, 84 continuity equation, 118 creation operator, 379 cyclic operator, 171 cyclic vector, 171 Darboux method, 435 Davisson and Germer, 33 de Broglie hypothesis, 30 Debye formula, 504 deficiency indices, 169 deficiency sub-spaces, 169 density matrix, 446 differential viewpoint, 529 diffraction of electrons, 7 Dirac notation, 172 representation, 552 direct sum of Hilbert spaces, 168 dispersion relation, 94 displacement law, 490 distance of rays, 473 double-slit experiment, 21 duality transformations, 420 Dulong and Petit law, 502 dynamical path, 528 Dyson series, 271 Ehrenfest theorem, 127 eikonal equation, 107 Einstein model of specific heats, 502 Einstein setting, 50 emission spectrum, 22 emissive power, 488 energy bands, 217 enveloping algebra, 82 ergodic, 483 Euclidean group, 77 Euler Lagrange equations, 84 exchange integral, 512 experiment of Phipps and Taylor, 229 extrinsic properties, 504 Fermat principle, 69 Fermi golden rule, 274 Fermi Dirac statistics, 508 Feynman formula, 536 first Landau level, 385 first-order pseudo-eigenvalue, 283 first-order pseudo-eigenvector, 283 flow of a dynamical system, 84 Fock space, 516 Fourier Dirichlet expansion, 544 Franck and Hertz, 26 Fredholm equation, 290 free Bose Einstein gas, 516 free Fermi Dirac gas, 518 Fresnel biprism, 17 Fuchs theorem, 223 Fuchsian singularity, 187 Galilean setting, 50 Galilei transformations, 132 Gamma-function, 224

3 590 gauge invariance, 241 Geiger and Nuttall, 160 Gel fand triple for the position and momentum observables, 371 Gel fand triples, 370 generalized energy equipartition law, 485 geometrical optics, 68 Gibbs measure, 482 global conservation property, 118 global viewpoint, 529 graph, 169 Green function, 139 ground state, 152 of harmonic oscillator, 381 group, 77 group velocity, 102, 108, 112 physical meaning, 103 gyromagnetic ratio, 227 Hamilton Jacobi equation, 52 harmonic oscillator, 375 harmonic polynomials, 205 Heisenberg algebra, 340 equations of motion, 362 microscope, 37 helium atom, 510 Helmholtz equation, 104 Hermite polynomials, 153 Hermitian, 169 hidden variables, 455 Hilbert space, 168 homomorphism of two groups, 211 Hulthén potential, 144 Husimi Kano distribution function, 547 hydrogen atom, 196 identical particles, 506 inner product, 168 space, 168 interference, 4 intrinsic properties, 504 isometry of ray space, 473 isospectral Hamiltonians, 435 Jacobi identity, 44 Jacobi polynomials, 425 JWKB solutions, 167 Kato Rellich theorem, 281 ket, 172 Kirchhoff theorem, 488 Kummer equation, 211 Lagrangian for the Schrödinger equation, 374 Landau levels, 383 Lebesgue decomposition of a measure, 140 Levinson theorem, 310 Lie algebra, 76 structure, 44 Lie derivative, 81 Lie group, 77 lift of a ray-space isometry, 474 linear potential, 186 Lippmann Schwinger equation, 304 local conservation law, 118 Lorentz group, 79 lowering operator, 400 Majorana representation, 552 Maupertuis principle, 69 mean value of the wavelength, 111 mean values, 125 microcanonical ensemble, 482 mixture, 449 modified Bessel functions, 225 momentum representation, 119 monopole harmonic, 424 Moyal bracket, 543 Moyal product, 543 Newton equations, 84 norm resolvent sense, 296

4 591 number operator, 378 observable quantity, 365 observation first kind, 367 second kind, 367 ortho-helium, 511 overlapofrays,473 Pancharatnam excess phase, 473 Pancharatnam lift, 473 para-helium, 511 parity operator, 360 Parseval lemma, 119 partial wave expansion, 309 partition function, 484 Paschen Back effect, 266 Pauli equation, 235 exclusion principle, 508 matrices, 213 perturbation theory for stationary states, 244 phase 1-form, 42 phase shifts, 308 phase velocity, 101 phonons, 408 photoelectric effect, 7 photons, 5 Planck radiation law, 496 Poincaré group, 79 Poincaré lemma, 46 point transformations, 85 Poisson bracket, 44 Poisson manifold, 44 polarization of light, 5 polydromy of the wave function, 315 populations, 463 principal function, 52 probability current, 118 projection postulate, 368 propagator, 139 pure case, 448 quantum entanglement, 460 quantum teleportation, 460 quantum tomogram, 547 quasi-exactly solvable systems, 430 radial quantum number, 164 Radon transform, 546 Radon Nykodim derivative, 484 raising operator, 400 Rayleigh Jeans radiation formula, 495 Rayleigh Ritz method, 266 reduced action, 72 reflection, 31, 176 Regge map, 416 regular perturbation theory, 280 residual coherences, 463 resolution of unity, 171 resolvent, 172, 296 set, 172, 296 resonance pole, 318, 319 resonant absorption, 272 resonant emission, 272 restricted three-body problem, 74 Riccati equation, 437 rigged Hilbert spaces, 370 Ritz combination principle, 25 Rollnik class, 306 rotation, 212, 358 Runge Lenz vector, 441 scattering matrix, 410 scattering operator, 300 Schrödinger equation, 113, 116 Schrödinger kernel, 138 Schwarz inequality, 168 Schwarz space, 376 semi-classical approximation, 160 singular perturbations, 284 singular potentials, 314 scattering, 314 spectral concentration, 283 spectral decomposition of a self-adjoint operator, 171

5 592 spectral family, 170 measure, 171 representation, 140 resolution, 170 spherical harmonics, 207 spin, 417 spin-j representation, 403 spreading in time, 142 standard deviations, 125 standard ordering, 534 Stark effect, 259 stationary phase method, 221 Stefan law, 490 step-like, 181 Stern and Gerlach, 227 Stirling formula, 520 Stone theorem, 343 strong continuity, 343 strong resolvent sense, 296 strongly asymptotic series, 281 strongly continuous one-parameter unitary group, 343 Sturm Liouville theorem, 311 SU(2) interferometer, 410 symbol, 93 symmetric, 169 symmetrization principle, 508 symplectic form, 46 symplectic manifold, 46 tensor product, 168 theory of electromagnetic signals, 523 Thomson scattering, 17 time reversal, 471 time-dependent formalism in perturbation theory, 269 time energy uncertainty relation, 354 topological group, 77 transformation operator, 437 translations, 358 transmission, 176 tunnelling effect, 184 two-photon coherent states, 393 uncertainty relations, 128, 351 unitary equivalence, 345 unitary transformation, 357 universal enveloping algebra, 82 vector field, 74, 75 vectors in phase, 473 virial theorem, 511 virtual state, 276 von Neumann theorem, 349 wave function vs. state vector, 269 wave operators, 302 weakly asymptotically complete, 299 Weyl system, 346, 347 width of a resonance, 318, 319 Wien, 490 Wigner distribution, 542 Wigner theorem, 469 Wintner theorem, 342 work done by a radiation field, 522 Zeeman effect, 266