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Simon B. — Quantum mechanics for Hamiltonians defined as quadratic forms
Simon B. — Quantum mechanics for Hamiltonians defined as quadratic forms

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Название: Quantum mechanics for Hamiltonians defined as quadratic forms

Автор: Simon B.

Аннотация:

It is our purpose in this monograph to present a complete, rigorous
mathematical treatment of two body quantum mechanics for a wider class
of potentials than is normally treated in the literature. At the same time,
we will review the theory of the "usual" Kato classes, although no attempt has been made to make this review exhaustive or complete. The
scope of what we present is best delineated by stating the limits of this
work: we take for granted the standard Hilbert space formalism, and our
main goal is to prove forward dispersion relations from first principles. For example we do not assume the Lippman-Schwinger equation but prove it within the framework of time-dependent scattering theory.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1971

Количество страниц: 244

Добавлена в каталог: 19.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L^2$-classes      viii
Approximation theorems, bound states      88—89
Approximation theorems, propagators      48
Approximation theorems, resolvants      48
Approximation theorems, S-matrices      112
Approximation theorems, spectral projections      48
Approximation theorems, wave operators      112
Asymptotic completeness      99 129
Asymptotic completeness, weak      99 105—110
Bargmann's bounds      89
Born series      15—22
Bound states, asymptotic behavior in      79 154—155
Bound states, bounds on the number of      85—89
Canonically cut plane      47
Closed operator      205
Cluster decomposition      180
Compact operators      217
Completeness of the wave operators      99 105—110 141
Contour pinching      168—171
Convergence, norm (operator)      202
Convergence, norm (vector)      202
Convergence, strong (operator)      202
Convergence, weak (operator)      203
Convergence, weak (vector)      202
Cook's theorem      102
Core      see domains of essential self-adjointness
Dispersion relations, forward      152—154
Dispersion relations, non-forward      159—160
Domains of essential self-adjointness      49 205
Eigenfunction expansions      115—126 133—135 138—143
Feynman path integral      50—53
Finite range potentials      24—26 130 155—173
Fredholm theorem, analytic      218
Ghirardi — Rimini bound      88—89
Green's function      72—77 118—120
Green's function, disconnected part      178—179
Green's function, reduced      184
Hack's theorem      103
Helium atom      194—196
Hilbert — Schmidt operators      220
Hughes — Eckart terms      190—194
Hunziker's theorem      185—186
Ikebe's theory      see eigenfunction expansions
Integral equation, bound state      79 80—85
Integral equation, factorized      20—21 148
Integral equation, Lippmann — Schwinger      117
Interpolation theorem, Hunt's      10
Interpolation theorem, Marcinkiewicz      9
Kato — Birman theorem      105—106
Kato — Rellich perturbation theory      69
Kato — Rellich theorem      206
Kato's theorem      32
Khuri conditions      147
Kisynski's theorems      56
Klein — Zemach theorem      23—24 95 1
KLMN theorem      41
Kupsch — Sandas theorem      104
Kuroda's approximation theorem      11
Legendre series, convergence of      162—165
Lehmann ellipse      160—161
Multiparticle Hamiltonian, definition of      174
Non-nasty potentials      6 18 36 147
Partial waves, analyticity of      163
Quadratic forms      33 38—45 215
refinement      181
Rollnik classes      3
Rollnik norm, $\parallel\:\parallel_R$      3
Scale of spaces      see quadratic forms
Schwinger's bound      86—87
Self adjoint operator      204
Self adjoint operator, essentially      205
Sobolev inequalities      4 9—12
Sobolev spaces      see quadratic forms
Spectral projections      213
Spectral theorem      207 213
Spectrum      208
Spectrum, absolutely continuous      210—211
Spectrum, discrete      214
Spectrum, essential      215
Spectrum, pure point      210—211
Spectrum, singular      101 130 210—211
Stone's theorem      216
String      181
T-matrix      143 152
Tiktopoulos' formula      45 47 175
Trace class      220
Trotter — Kato theorem      217
Trotter's theorem      217
Unitary propagator      53
Wave operators      94 97—99 102—110
Wave operators, Dollard      110
Weinberg — Van Winter expansion      175—179
Weinberg — Van Winter expansion, factorized      179—185
Weyl's min-max principle      71
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