Amazon cover image
Image from Amazon.com
Image from Coce

Determining spectra in quantum theory/ Michael Demuth, M. Krishna.

By: Contributor(s): Material type: TextPublication details: Boston : Birkhäuser, c2005.Description: x, 219 p. ; 25 cmISBN:
  • 9780817643669
Subject(s): DDC classification:
  • 515.7222  DEM/D
Contents:
1 Measures and Transforms ................................. 1 1.1 Measures .............. ................................. 1 1.2 Fourier Transform ..................................... 5 1.3 The Wavelet Transform ................................. 7 1.4 Borel Transform .................. ...................... 16 1.5 Gesztesy-Krein-Simon Function ......................... 24 1.6 Notes ................. ............. ............ 25 2 Selfadjointness and Spectrum .............................. 29 2.1 Selfadjointness ........................... ............. 29 2.1.1 Linear Operators and Their Inverses ................. 29 2.1.2 Closed Operators ..................... .......... 30 2.1.3 Adjoint and Selfadjoint Operators ................... 32 2.1.4 Sums of Linear Operators .......................... 34 2.1.5 Sesquilinear Forms ................................ 35 2.2 Spectrum and Resolvent Sets ............................. 37 2.3 Spectral Theorem ..................................... 40 2.4 Spectral Measures and Spectrum .................. ....... 43 2.5 Spectral Theorem in the Hahn-Hellinger Form .............. 45 2.6 Components of the Spectrum ............................. 49 2.7 Characterization of the States in Spectral Subspaces ......... 53 2.8 Notes ................. ................... .......... 56 3 Criteria for Identifying the Spectrum ...................... 59 3.1 Borel Transform ...................................... 59 3.2 Fourier Transform ..................................... 68 3.3 Wavelet Transform ..................................... 69 3.4 Eigenfunctions ....................................... 70 3.5 Commutators ............................ ........... 72 3.6 Criteria Using Scattering Theory ....................... .. 80 3.6.1 Wave Operators .................................. 81 3.6.2 Stability of the Absolutely Continuous Spectra ........ 95 3.7 Notes .................................. ............104 4 Operators of Interest ...................................... 111 4.1 Unperturbed Operators ............... ............... . 111 4.1.1 Laplacians ..................... .................112 4.1.2 Unperturbed Semigroups and Their Kernels ..........119 4.1.3 Associated Processes . ........................... 120 4.1.4 Regular Dirichlet Forms, Capacities and Equilibrium Potentials ......................... ..............121 4.2 Perturbed Operators ................ .................. 125 4.2.1 Deterministic Potentials ......................... . 125 4.2.2 Random Potentials ............................. . 133 4.2.3 Singular Perturbations .......................... . 135 4.3 Notes ................ .............................142 5 Applications .............................................153 5.1 Borel Transforms .......................................153 5.1.1 K otani Theory .................................... 153 5.1.2 Aizenman-Molchanov Method ...................... 160 5.1.3 Bethe Lattice ..................................... 172 5.1.4 Jaksid-Last Theorem ........................... . 181 5.2 Scattering ..........................................183 5.2.1 Decaying Random Potentials. ..................... .183 5.2.2 Obstacles and Potentials ........................ . 187 5.3 Notes ................................................196
Tags from this library: No tags from this library for this title. Log in to add tags.
Star ratings
    Average rating: 0.0 (0 votes)
Holdings
Cover image Item type Current library Home library Collection Shelving location Call number Materials specified Vol info URL Copy number Status Notes Date due Barcode Item holds Item hold queue priority Course reserves
General Books Central Library, Sikkim University General Book Section 515.7222 DEM/D (Browse shelf(Opens below)) Available P19627
Total holds: 0

Includes bibliographical references (p. [203]-213) and index.

1 Measures and Transforms ................................. 1
1.1 Measures .............. ................................. 1
1.2 Fourier Transform ..................................... 5
1.3 The Wavelet Transform ................................. 7
1.4 Borel Transform .................. ...................... 16
1.5 Gesztesy-Krein-Simon Function ......................... 24
1.6 Notes ................. ............. ............ 25
2 Selfadjointness and Spectrum .............................. 29
2.1 Selfadjointness ........................... ............. 29
2.1.1 Linear Operators and Their Inverses ................. 29
2.1.2 Closed Operators ..................... .......... 30
2.1.3 Adjoint and Selfadjoint Operators ................... 32
2.1.4 Sums of Linear Operators .......................... 34
2.1.5 Sesquilinear Forms ................................ 35
2.2 Spectrum and Resolvent Sets ............................. 37
2.3 Spectral Theorem ..................................... 40
2.4 Spectral Measures and Spectrum .................. ....... 43
2.5 Spectral Theorem in the Hahn-Hellinger Form .............. 45
2.6 Components of the Spectrum ............................. 49
2.7 Characterization of the States in Spectral Subspaces ......... 53
2.8 Notes ................. ................... .......... 56
3 Criteria for Identifying the Spectrum ...................... 59
3.1 Borel Transform ...................................... 59
3.2 Fourier Transform ..................................... 68
3.3 Wavelet Transform ..................................... 69
3.4 Eigenfunctions ....................................... 70
3.5 Commutators ............................ ........... 72
3.6 Criteria Using Scattering Theory ....................... .. 80
3.6.1 Wave Operators .................................. 81
3.6.2 Stability of the Absolutely Continuous Spectra ........ 95
3.7 Notes .................................. ............104
4 Operators of Interest ...................................... 111
4.1 Unperturbed Operators ............... ............... . 111
4.1.1 Laplacians ..................... .................112
4.1.2 Unperturbed Semigroups and Their Kernels ..........119
4.1.3 Associated Processes . ........................... 120
4.1.4 Regular Dirichlet Forms, Capacities and Equilibrium
Potentials ......................... ..............121
4.2 Perturbed Operators ................ .................. 125
4.2.1 Deterministic Potentials ......................... . 125
4.2.2 Random Potentials ............................. . 133
4.2.3 Singular Perturbations .......................... . 135
4.3 Notes ................ .............................142
5 Applications .............................................153
5.1 Borel Transforms .......................................153
5.1.1 K otani Theory .................................... 153
5.1.2 Aizenman-Molchanov Method ...................... 160
5.1.3 Bethe Lattice ..................................... 172
5.1.4 Jaksid-Last Theorem ........................... . 181
5.2 Scattering ..........................................183
5.2.1 Decaying Random Potentials. ..................... .183
5.2.2 Obstacles and Potentials ........................ . 187
5.3 Notes ................................................196

There are no comments on this title.

to post a comment.
Previous
Back to results
Next
Close
SIKKIM UNIVERSITY
University Portal | Contact Librarian | Library Portal