Verfügbarkeit: Determining spectra in quantum theory

Gespeichert in:

Bibliographische Detailangaben
Beteiligte Personen:	Demuth, Michael 1946- (VerfasserIn), Krishna, Maddaly (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Boston [u.a.] Birkhäuser 2005
Schriftenreihe:	Progress in mathematical physics 44
Schlagwörter:	Operator theory Potential theory (Mathematics) Scattering (Mathematics) Spectral theory (Mathematics) Selbstadjungierter Operator Hamilton-Operator Spektraltheorie
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013354431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013354431&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	X, 219 S.
ISBN:	0817643664 9780817643669

Internformat

MARC


LEADER	00000nam a2200000 cb4500
001	BV020033243
003	DE-604
005	20090721
007	t\|
008	050915s2005 xx \|\|\|\| 00\|\|\| eng d
015			\|a 04,N36,0405 \|2 dnb
016	7		\|a 971959838 \|2 DE-101
020			\|a 0817643664 \|c Gb. \|9 0-8176-4366-4
020			\|a 9780817643669 \|9 978-0-8176-4366-9
024	3		\|a 9780817643669
028	5	2	\|a 11006008
035			\|a (OCoLC)60321621
035			\|a (DE-599)BVBBV020033243
040			\|a DE-604 \|b ger \|e rakddb
041	0		\|a eng
049			\|a DE-824 \|a DE-384 \|a DE-91G \|a DE-29T \|a DE-20 \|a DE-355 \|a DE-11
050		0	\|a QA404.7
082	0		\|a 515/.7222 \|2 22
084			\|a SK 620 \|0 (DE-625)143249: \|2 rvk
084			\|a SK 950 \|0 (DE-625)143273: \|2 rvk
084			\|a 530 \|2 sdnb
084			\|a PHY 013f \|2 stub
084			\|a MAT 470f \|2 stub
100	1		\|a Demuth, Michael \|d 1946- \|e Verfasser \|0 (DE-588)130367478 \|4 aut
245	1	0	\|a Determining spectra in quantum theory \|c Michael Demuth ; M. Krishna
264		1	\|a Boston [u.a.] \|b Birkhäuser \|c 2005
300			\|a X, 219 S.
336			\|b txt \|2 rdacontent
337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
490	1		\|a Progress in mathematical physics \|v 44
650		4	\|a Operator theory
650		4	\|a Potential theory (Mathematics)
650		4	\|a Scattering (Mathematics)
650		4	\|a Spectral theory (Mathematics)
650	0	7	\|a Selbstadjungierter Operator \|0 (DE-588)4180810-1 \|2 gnd \|9 rswk-swf
650	0	7	\|a Hamilton-Operator \|0 (DE-588)4072278-8 \|2 gnd \|9 rswk-swf
650	0	7	\|a Spektraltheorie \|0 (DE-588)4116561-5 \|2 gnd \|9 rswk-swf
689	0	0	\|a Hamilton-Operator \|0 (DE-588)4072278-8 \|D s
689	0	1	\|a Selbstadjungierter Operator \|0 (DE-588)4180810-1 \|D s
689	0	2	\|a Spektraltheorie \|0 (DE-588)4116561-5 \|D s
689	0		\|5 DE-604
700	1		\|a Krishna, Maddaly \|e Verfasser \|4 aut
830		0	\|a Progress in mathematical physics \|v 44 \|w (DE-604)BV013823265 \|9 44
856	4	2	\|m Digitalisierung UB Regensburg \|q application/pdf \|u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013354431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA \|3 Inhaltsverzeichnis
856	4	2	\|m Digitalisierung UB Regensburg \|q application/pdf \|u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013354431&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA \|3 Klappentext
943	1		\|a oai:aleph.bib-bvb.de:BVB01-013354431

Datensatz im Suchindex

DE-BY-TUM_call_number	0202 PHY 013f 2005 A 9135
DE-BY-TUM_katkey	1529085
DE-BY-TUM_location	02
DE-BY-TUM_media_number	040020747002
DE-BY-UBR_call_number	80/SK 950 D389
DE-BY-UBR_katkey	4504155
DE-BY-UBR_location	UB Lesesaal Mathematik
DE-BY-UBR_media_number	069037161897
_version_	1835087181143605249
adam_text	Contents Preface v 1 Measures and Transforms .................................. 1 1.1 Measures ............................................... 1 1.2 Fourier Transform ....................................... 5 1.3 The Wavelet Transform .................................. 7 1.4 Borei Transform ......................................... 16 1.5 Gesztesy-Krein-Simon ξ 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 Borei Transform ........................................ 59 3.2 Fourier Transform ....................................... 68 3.3 Wavelet Transform ...................................... 69 3.4 Eigenfunctions .......................................... 70 3.5 Commutators .......................................... 72 χ Contents 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 ...................................... Ill 4.1 Unperturbed Operators .................................. Ill 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 Borei Transforms ........................................153 5.1.1 Kotani Theory ....................................153 5.1.2 Aizenman-Molchanov Method ......................160 5.1.3 Bethe Lattice .....................................172 5.1.4 Jaksić-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 References .....................................................203 Index ..........................................................215 Michael Demuth and M. Krishna Determining Spectra in Quantum Theory The spectral theory of Schrodinger operators, in particular those with random potentials, continues to be a very active field of research. This work focuses on various known criteria in the spectral theory ol sell adjoint operators in order to identify the spectrum and its components à la I.ebesgue decomposition. Key features and topics: • Well-developed exposition of criteria that are especially useful in determining the spectra of deterministic and random Schrodinger operators occurring in quantum theory • Systematically uses measures and their transforms ( Fourier. Borei, wavelet ) to present a unifying theme • Establishes criteria for identifying the spectrum • Examines a series of applications to show point spectrum and continuous spectrum in some models of random operators • Presents a series of spectral-theoretic results for the perturbed operator» introduced in the earlier chapters with examples of localization and delocalization in the theory of disordered systems • Presents modern criteria (using wavelet transform, eigenfunction decav ι that could be used to do spectral theory • Unique work in book form combining the presentation of the deterministic and random cases, which will serve as a platform for further research activities This concise unified presentation is aimed at graduate students and researchers working in the spectral theory of Schrodinger operators with either fixed or random potentials in particular. However, given the large gap that this book fills in the literature, it will serve a wider audience of mathematical phvsicists in its contribution to works in spectral theory.
any_adam_object	1
author	Demuth, Michael 1946- Krishna, Maddaly
author_GND	(DE-588)130367478
author_facet	Demuth, Michael 1946- Krishna, Maddaly
author_role	aut aut
author_sort	Demuth, Michael 1946-
author_variant	m d md m k mk
building	Verbundindex
bvnumber	BV020033243
callnumber-first	Q - Science
callnumber-label	QA404
callnumber-raw	QA404.7
callnumber-search	QA404.7
callnumber-sort	QA 3404.7
callnumber-subject	QA - Mathematics
classification_rvk	SK 620 SK 950
classification_tum	PHY 013f MAT 470f
ctrlnum	(OCoLC)60321621 (DE-599)BVBBV020033243
dewey-full	515/.7222
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	515 - Analysis
dewey-raw	515/.7222
dewey-search	515/.7222
dewey-sort	3515 47222
dewey-tens	510 - Mathematics
discipline	Physik Mathematik
format	Book
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02450nam a2200589 cb4500</leader><controlfield tag="001">BV020033243</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20090721 </controlfield><controlfield tag="007">t\|</controlfield><controlfield tag="008">050915s2005 xx \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">04,N36,0405</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">971959838</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0817643664</subfield><subfield code="c">Gb.</subfield><subfield code="9">0-8176-4366-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780817643669</subfield><subfield code="9">978-0-8176-4366-9</subfield></datafield><datafield tag="024" ind1="3" ind2=" "><subfield code="a">9780817643669</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">11006008</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)60321621</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV020033243</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-824</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA404.7</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.7222</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 620</subfield><subfield code="0">(DE-625)143249:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">530</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PHY 013f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 470f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Demuth, Michael</subfield><subfield code="d">1946-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)130367478</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Determining spectra in quantum theory</subfield><subfield code="c">Michael Demuth ; M. Krishna</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston [u.a.]</subfield><subfield code="b">Birkhäuser</subfield><subfield code="c">2005</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 219 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Progress in mathematical physics</subfield><subfield code="v">44</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Operator theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Potential theory (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Scattering (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Spectral theory (Mathematics)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Selbstadjungierter Operator</subfield><subfield code="0">(DE-588)4180810-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Hamilton-Operator</subfield><subfield code="0">(DE-588)4072278-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Spektraltheorie</subfield><subfield code="0">(DE-588)4116561-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Hamilton-Operator</subfield><subfield code="0">(DE-588)4072278-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Selbstadjungierter Operator</subfield><subfield code="0">(DE-588)4180810-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Spektraltheorie</subfield><subfield code="0">(DE-588)4116561-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Krishna, Maddaly</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Progress in mathematical physics</subfield><subfield code="v">44</subfield><subfield code="w">(DE-604)BV013823265</subfield><subfield code="9">44</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013354431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013354431&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Klappentext</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-013354431</subfield></datafield></record></collection>
id	DE-604.BV020033243
illustrated	Not Illustrated
indexdate	2024-12-20T12:10:38Z
institution	BVB
isbn	0817643664 9780817643669
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-013354431
oclc_num	60321621
open_access_boolean
owner	DE-824 DE-384 DE-91G DE-BY-TUM DE-29T DE-20 DE-355 DE-BY-UBR DE-11
owner_facet	DE-824 DE-384 DE-91G DE-BY-TUM DE-29T DE-20 DE-355 DE-BY-UBR DE-11
physical	X, 219 S.
publishDate	2005
publishDateSearch	2005
publishDateSort	2005
publisher	Birkhäuser
record_format	marc
series	Progress in mathematical physics
series2	Progress in mathematical physics
spellingShingle	Demuth, Michael 1946- Krishna, Maddaly Determining spectra in quantum theory Progress in mathematical physics Operator theory Potential theory (Mathematics) Scattering (Mathematics) Spectral theory (Mathematics) Selbstadjungierter Operator (DE-588)4180810-1 gnd Hamilton-Operator (DE-588)4072278-8 gnd Spektraltheorie (DE-588)4116561-5 gnd
subject_GND	(DE-588)4180810-1 (DE-588)4072278-8 (DE-588)4116561-5
title	Determining spectra in quantum theory
title_auth	Determining spectra in quantum theory
title_exact_search	Determining spectra in quantum theory
title_full	Determining spectra in quantum theory Michael Demuth ; M. Krishna
title_fullStr	Determining spectra in quantum theory Michael Demuth ; M. Krishna
title_full_unstemmed	Determining spectra in quantum theory Michael Demuth ; M. Krishna
title_short	Determining spectra in quantum theory
title_sort	determining spectra in quantum theory
topic	Operator theory Potential theory (Mathematics) Scattering (Mathematics) Spectral theory (Mathematics) Selbstadjungierter Operator (DE-588)4180810-1 gnd Hamilton-Operator (DE-588)4072278-8 gnd Spektraltheorie (DE-588)4116561-5 gnd
topic_facet	Operator theory Potential theory (Mathematics) Scattering (Mathematics) Spectral theory (Mathematics) Selbstadjungierter Operator Hamilton-Operator Spektraltheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013354431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013354431&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV013823265
work_keys_str_mv	AT demuthmichael determiningspectrainquantumtheory AT krishnamaddaly determiningspectrainquantumtheory

Verfügbarkeit

Bestellen (Login erforderlich)

Inhaltsverzeichnis
Paper/Kapitel scannen lassen

Teilbibliothek Physik

Bestandsangaben von Teilbibliothek Physik
Signatur:	0202 PHY 013f 2005 A 9135
Exemplar 1	Ausleihbar Am Standort