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Araki H. (ed.), Ezawa H. (ed.) — Topics in the Theory of Schrödinger Operators
Araki H. (ed.), Ezawa H. (ed.) — Topics in the Theory of Schrödinger Operators



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Название: Topics in the Theory of Schrödinger Operators

Авторы: Araki H. (ed.), Ezawa H. (ed.)

Аннотация:

This book presents reviews of some recent topics in the theory of Schrodinger operators. It includes a short introduction to the subject, a survey of the theory of the Schrodinger equation when the potential depends on the time periodically, an introduction to the so-called FBI transformation (also known as coherent state expansion) with application to the semi-classical limit of the S-matrix, an overview of inverse spectral and scattering problems, and a study of the ground state of the Pauli-Fierz model with the use of the functional integral. The material is accessible to graduate students and non-expert researchers.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 275

Добавлена в каталог: 12.01.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$H$-smooth      27
$n$-resonant solution      34
$S$-matrix      99
Annihilation operator      156
Araki — Woods representation      150
Asymptotic completeness      115 198
Asymptotic completeness for Rayleigh scattering      198
Asymptotic field      191
Autonomous case      11
Birman’s invariance principle      79
Bogoliubov transformation      185
Borg — Levinson theorem      106
Born approximation      113 115
Boson density      263
Boson Fock space      155
Bound state      2
Boundary spectral data (BSD)      109
Brownian motion      205
Burkholder inequality      214
Canonical commutation relation      156
Carmona’s estimate      240
Charge density      239
Coherent state expansion      71
Completeness      25
Completeness of wave operators      5
Coulomb gauge      154
Creation operator      156
Degenerate ground state      227
Diamagnetic inequality      221 239 256
Differential cross section      98
Dilation analytic method      53
Dilation analyticity      50
Dipole approximation      145 166 184 197
Dirichlet — Neumann map      135
Double commutation      97
Duhamel formulae      40
effective mass      242
Enhanced binding      184
Essentially self-adjoint      12
Essentially self-adjoint ness      11
Exceptional type      34
Excited states      2
Exponential weight estimate      76
External force      9
Faddeev scattering amplitude      127
Faddeev theory      129
Faddeev’s Green operator      118
FBI transform      71 75
FBI-quantized operator      75
Fermi Golden Rule      49 56
Field momentum      230
Floquet Hamiltonian      19 20
Fock representation      155
Fock vacuum      156
Functional integral representation      198 206 221
Gaussian random process      199 202 203 253
Gel’fand problem      108
Gel’fand — Levitan equation      103 120 132
Gel’fand — Levitan theory      100
Generalized Gel’fand problem      108 109
Generalized sine transformation      102
Generic type      34
Hille — Yoshida theorem      211
Infinite volume Gibbs measure      244
Infrared cutoff condition      163
Infrared divergence      162
Infrared regularity condition      163
Infrared singularity      162
Instability      49
Integral operator of $Volterra$ type      104
Intertwining property      26
Inverse back scattering      116
Inverse conductivity problem      135
Inverse eigenvalue problem      94
Inverse scattering      31 98 116
Inverse scattering at a fixed energy      128
Inverse spectral theory      93
Isospectral deformation      96
Isospectral manifold      112
Isospectral potentials      95
Kac problem      111
KMS state      149
Kolmogorov Extension Theorem      245
Kolmogorov theorem      258
Lamb shift      146
Lebesgues space      10
Lieb — Thirring identity      191
Liouvillean      149
Local decay property      33
Markov property      208
Mass renormalization      242
Maximal operator      12
Maxwell equation      153
Method of integral equation      14
Minimal operator      12
Minlos theorem      199
Mourre theory      23
Multistate scattering theory      71
Nelson Hamiltonian      252
Nonautonomous case      13
Nontrapping      73
Number operator      159 200 204 258
Overdeterminacy      113 115
Paley — Wiener theorem      103 119
Pauli — Fierz Hamiltonian      160
Pauli — Fierz Hamiltonian with a fixed total momentum      231
Perturbed Green operator      122 126
Phase space tunneling      71
Positivity improving operator      222
Positivity preserving operator      221
Propagator      11
Pseudodifferential operator      73
Pull-through formula      167 181 196 233
Quantized radiation field      160
RAGE theorem      24
Real analytic      96
Resolvent set      10
Scaling limit      194
Scattering amplitude      98
Scattering matrix      31 73 78
Scattering operator      4 30 98
Scattering theory      24
Schrodinger operator      1
Schrodinger representation      199
Second quantization      158
Semigroup theory      13
Slowly decreasing potential      129
Sobolev space of order s      10
Spectral invariant      112
Spectral projection      10
Spectral representation      116
Spectrum      10
Stone theorem      11 275
Strichartz estimates      38
Strichartz inequality      15
Symplectic group      185
Theorem of Borg — Levinson      94
Threshold resonance      34
Time dependent Schr$\ddot{o}$dinger equation      9
Total momentum      230
Translation invariance      230
Trotter — Kato product formula      207 209 256
Two-state Schrodinger operator      71
Ultraviolet cutoff      160
Volterra integral operator      117
Volterra operator      131
Wave operator      4 25 81 84
Weak coupling limit      195
Weighted $L^{2}$ space      10
Wellposed      11
Wick product      200
Wiener measure      205
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