Berezin F.A., Shubin M.A. — The Schroedinger equation :: Электронная библиотека попечительского совета мехмата МГУ

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Berezin F.A., Shubin M.A. — The Schroedinger equation

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Название: The Schroedinger equation

Авторы: Berezin F.A., Shubin M.A.

Аннотация:

The Schrodinger equation is the basic equation of quantum theory. The study of this equation plays an exceptionally important role in modern physics. From a mathematician's point of view the Schrodinger equation is as inexhaustible as mathematics itself.
In this book an attempt has been made to set forth those topics of mathematical physics, associated with the study of the Schrodinger equation, which appear to be the most important.

Язык:

Рубрика: Математика/Математическая Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 576

Добавлена в каталог: 23.04.2005

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Предметный указатель

      490
$H^{s}(\mathbf{R}^{n})$       468
$H^{s}(\Omega)$       466
$H^{s}_{N}(\mathbf{R}^{n})$       161
      492
      493
-symbol      285 291
-symbol      285
      517
$W\PM(H,H_{0}$       224
$\mathfrak{ab}(n)$       517
$\mathfrak{b}(n)$       501
$\mathfrak{gl}$ (n|m)$      499
$\mathfrak{GL}(p|q)$       508
$\mathfrak{hei}(2n)$       511
$\mathfrak{h}(2n|m)$       502
$\mathfrak{l}(2n + l|m)$       501
$\mathfrak{m}(n)$       501
$\mathfrak{osp}(n|2m)$       500
$\mathfrak{pe}(n)$       500
$\mathfrak{po}(2n|m)$       501
$\mathfrak{sm}(n)$       501
$\mathfrak{sve}(n|m)$       500
$\mathfrak{vect}(n|m)$       500
A priori estimate      475
Anti - Wick normal form      307
Anti - Wick symbol      308
Asymptotics, semi-classical      374
Band functions      138 211
Berezinian      490
Bloch function      135 200
Bohr's formula      385
Bose - Einstein statistics      41
Boson      32 41
Brillouin zone      135
Canonical anticommutation relations      49
Canonical commutation relations      46
Canonical transformation, linear      300
Chain rule      231
Commuting self-adjoint operators      407
Contravariant symbol      317
Cook's criterion      235
Correspondence principle      283
Courant's minimax principle      440
Covariant symbol      317
de Broglie wave      29
Density of states      211
Dirichlet boundary condition      87
Discrete spectrum      57
Eigenfunctions      see Eigenvectors
Eigenvectors, generalized      426
Eigenvectors, generalized, complete system of      426
Energy operator      6
Evolution operator      6
Exterior algebra      488
Fermi - Dirac statistics      41
Fermion      32 42
Feynman path integral      325
Fock space      45
Form, bilinear      491
Form, bilinear, skewsymmetric      491
Form, bilinear, symmetric      491
Form, closed      498
Form, differential      497
Form, differential, exterior      497
Form, exact      498
Form, integrable      497
Form, pseudodifferential      497
Form, pseudointegrable      497
Form, volume      497
functor      495
Functor of points      495
Functor, representing      495
General linear group      490
Glazman's lemma      435
Green's function      110 178 480
Group, orthosymplectic      492
Group, peculiar (periplectic) unitary      493
Group, projective of type       494
harmonic oscillator      33
Heaviside function      71
Heisenberg algebra $\mathfrak{hei}(2n)$       511
Heisenberg commutation relations      19
Heisenberg picture      15
Heisenberg uncertainty relations      24
Hermite function      36
Hermite polynomial      36
Hilbert space      386
Hilbert space, th antisymmetric power of      464
Hilbert space, th symmetric power of      464
Hilbert space, rigged      425
Hilbert space, rigging of      425
Hilbert space, rigging of, Hilbert - Schmidt      425
Hilbert spaces, tensor product of      462
Homogeneous elements      487
Isometry      393
Jost functions      122
Lattice      198
Lattice, Brillouin zone of      199
Lattice, dual      199
Lattice, dual, unit cell of      199
Lie superalgebra      499 507
Lie superalgebra, Buttin $\mathfrak{b}(n)$       501
Lie superalgebra, Buttin $\mathfrak{b}(n)$ , special $\mathfrak{sb}(n)$       501
Lie superalgebra, contact $\mathfrak{l}(2n + l|m)$       501
Lie superalgebra, contact $\mathfrak{l}(2n + l|m)$ , odd $\mathfrak{m}(n)$       501
Lie superalgebra, contact $\mathfrak{l}(2n + l|m)$ , special odd s $\mathfrak{sm}(n)$ m(n)      501
Lie superalgebra, divergence-free vectory $\mathfrak{sve}(n|m)$       500
Lie superalgebra, general linear $\mathfrak{gl}(n|m)$       499
Lie superalgebra, general vectory $\mathfrak{vect}(n|m)$       500
Lie superalgebra, left module over      488
Lie superalgebra, of Hamiltonian fields $\mathfrak{h}(2n|m)$       503
Lie superalgebra, orthosymplectic $\mathfrak{osp}(n|2m)$       500
Lie superalgebra, peculiar (perplectic) $\mathfrak{pe}(n)$       500
Lie superalgebra, projective of type $\mathfrak{gl}$       500
Lie superalgebra, right module over      488
Lie superalgebra, special linear $\mathfrak{sl}(n|m)$       499
Lie superalgebra, special vectory $\mathfrak{sve}(n|m)$       500
Lie superalgebra, universal enveloping algebra of      488
Lie supergroup      507
Lie supergroup, general linear $\mathfrak{GL}(p|g)$       508
Liouville transformation      82
Lippman - Schwinger equations      261
Majorizing integral function      76
Marchenko equation      129
Measure space      393
Minimax principle      440
Module      489
Module, dual      489
Module, free      489
Module, indecomposble      489
Module, irreducible      489
Module, irreducible, of -type      489
Monodromy matrix      136
Morphism of ringed spaces      494
Morphism of sheaves      494
Multiplier      135
Neumann boundary condition      94
Observable      4
Observable, canonically conjugate      24
Observable, jointly measurable      5
Observable, mean value of      9
Observable, time-derivative      16
Observable, time-differentiable      16
Observable, variance of      10
Observables, complete set of      26
Observables, simultaneously measurable      5
Occupation numbers      305
One-parameter group      414
One-parameter group of unitary operators      414

Operator, adjoint      388
Operator, annihilation      35 46 304
Operator, closable      388
Operator, closed      388
Operator, closure of      388
Operator, creation      35 46 304
Operator, density      14
Operator, essentially self-adjoint      389
Operator, extension of      388
Operator, graph of      387
Operator, Hilbert - Schmidt      420 (see also Hilbert space rigging)
Operator, inverse      387
Operator, isometry      393
Operator, Laplace - Beltrami      184
Operator, linear      387
Operator, linear, domain of      387
Operator, momentum      18 27
Operator, multiplication      394
Operator, nuclear      449
Operator, orbital      31
Operator, polar decomposition of      451
Operator, position      18
Operator, resolvent of      390
Operator, scattering      224 362
Operator, Schr $\ddot{o}$ dinger      18
Operator, self-adjoint      389
Operator, spectrum of      390
Operator, spin      31
Operator, spur of      449
Operator, symmetric      389
Operator, tensor product      463
Operator, trace class      449
Operator, trace norm of      453
Operator, trace of      449
Operator, translation      134
Operator, unitary      393 (see also One-parameter group)
Operator, wave      224
Operator, wave, completeness of      225
Overfilled system of vectors      316
Parity      487
Particle      27
Particle, boson      32 41
Particle, fermion      32 42
Particle, identity principle      41
Particle, number operator      45
Particle, total angular momentum      32
Particle, with spin      30
Partition function      370
Pauli's exclusion principle      44
Planck's constant      1 6
Poisson - Lie bracket      510
Poisson bracket      17
Poisson vector      308
Polarization identity      398
Pseudodifferential form      497
Quantization      19 282
Quantum particle      27
Quantum particle, free scalar      27
Quasi-momentum      135 200
Quasi-momentum, monotonic      127
Rayleigh relation      443
Reflection coefficient      123
Representation      21 489
Representation momentum      21
Representation position      21
Representation spinor      516
Resolvent set      390
Riesz projection      441
Ringed space      494
Ringed space morphism      494
Scattering data      130
Scattering matrix      133 249
Scattering operator      224 362
Schr $\ddot{o}$ dinger equation      6
Schr $\ddot{o}$ dinger operator      18
Schr $\ddot{o}$ dinger picture      15
Schr $\ddot{o}$ dinger time-independent      11
Sear's Theorem      50
Sheaf      494
Sheaf, direct image of      494
Sheaf, isomorphism      494
Sheaf, morphism      494
Sheaf, of groups      494
Sign rule      487
Sobolev embedding theorem      469
Sobolev space      161 466 468
Sobolev trace theorem      470
Sommerfeld's radiation condition      280
Special linear groups ,       491
Spectral family      394
Spectrum      see operator spectrum
Spectrum, absolutely continuous      418
Spectrum, allowed zone of      141 213
Spectrum, essential      182
Spectrum, forbidden zone of      141 213
Spectrum, gap of      141 213
Spectrum, lacuna of      141 213
Spectrum, point      418
Spectrum, simple      409
Spectrum, simple joint      409
Spectrum, singular continuous      418
Spectrum, zone of      141 213
Spherical harmonics      30
Standard format      489
State      4
State, coherent      308
State, mixed      14
State, space      5
State, stationary      11
State, vector      5
Strongly continuous      414
Sturm oscillation theorem      59
Superalgebra      487
Superalgebra, antibracket $\mathfrak{ab}(n)$       517
Superalgebra, commutative      487
Superalgebra, Lie      see Lie superalgebra
Superalgebra, of observables      515
Superalgebra, Poisson $\mathfrak{po}(2n|m)$       501
Superalgebra, representation      489
Superalgebra, Schouten       517
Superalgebra, stringy      504
Supercommutator      487
Superdomain of dimension       496
Supergroup of diffeomorphisms      496
Supermanifold, coordinate system of      496
Supermanifold, linear of dimension       496
Supermanifold, smooth      495
Supermanifold, smooth, base of      495
Supermanifold, smooth, closed subsuperdomain in      498
Supermanifold, smooth, underlying manifold of      495
Supermanifold, vector field on      497
Supermatrix      489
Superselection rules      7
Superspace      487
Superspace morphism      487
Supertrace      490
Symmetric algebra      487
Tensor algebra      487
Tensor product of Hilbert spaces      462
Tensor product of operators      463
Transmission coefficient      123
Upsetting of forms      491
Vector, cyclic      409
Vector, vacuum      47
Volume      497
Wave function      20
Wave function in the momentum representation      21
Weyl algebra      512
Weyl symbol      294
Wick normal form      307

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