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Hilbert Space Operators Pdf Free
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Hilbert Space Operators Pdf Free
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64,,[Ebook][Buddha][Buddhism],,-,,Buddhist,,Medit.,,Eckmann,,Department,of,Theoretical,Physics,,University,of,Geneva,,SwitzerlandH.,0/100,,.,With,this,fact,in,mind,,we,were,naturallypleased,to,learn,that,the,volum12345>,www.taodocs.com..,..,,Loss,,,School,,of,,Mathematics,,,ia,,Institute,,of,,Technology,,,Atlanta,,,GA,,,USAS.,,Mathemat-ical,,physics,,of,,quantum,,systems,,remains,,a,,lively,,subject,,of,,intrinsic,,interest,,withnumerous,,applications,,,both,,actual,,and,,potential.In,,the,,preface,,to,,the,,?rst,,edition,,we,,have,,described,,the,,origin,,of,,this,,book,,rootedat,,the,,beginning,,in,,a,,course,,of,,lectures.,,
Thewider,scope,of,the,series,is,re?ected,by,position,of,the,editorial,board,,comprisingboth,physicists,and,mathematicians.The,books,,written,in,a,didactic,style,and,containing,a,certain,amount,of,elementary,back-ground,materials,,bridge,the,gap,between,advanced,textbooks,and,research,monographs.They,can,thus,serve,as,basis,for,advanced,studies,,not,only,for,lectures,and,seminars,atgraduate,level,,but,also,for,scientists,entering,a,?eld,of,research.Editorial,BoardW.,1184,,[hH.Rosen]bin,,196,,[Go,,Baduk,,Igo,,Weiqi],,fr,,-Les,,bases,,techniq.,,Yngvason,,,,Institute,,,of,,,Theoretical,,,Physics,,,,University,,,of,,,Vienna,,,,AustriaJir,,,Blank?Pavel,,,Exner?Miloslav,,,HavlcekHilbert,,,Space,,,Operatorsin,,,Quantum,,,PhysicsSecond,,,EditionABCJir,,,Blank?PragueCzechiaPavel,,,ExnerDoppler,,,InstituteBrehov,,,711519,,,Pragueand,,,Nuclear,,,Physics,,,InstituteCzech,,,Academy,,,of,,,Sciences25068Rez,,,near,,,PragueCzech,,,Republicexnerujf.cas.czMiloslav,,,HavlcekDoppler,,,Instituteand,,,Faculty,,,of,,,Nuclear,,,Sciencesand,,,Physical,,,EngineeringCzech,,,Technical,,,UniversityTrojanova,,,1312000,,,PragueCzech,,,Republichavlicekfj?.cvut.czISBN,,,978-1-4020-8869-8,,,e-ISBN,,,978-1-4020-8870-4Library,,,of,,,Congress,,,Control,,,Number:,,,2008933703All,,,Rights,,,Reservedc?2008,,,Springer,,,Science,,,+Business,,,Media,,,B.V.c?1993,,,,?rst,,,edition,,,,AIP,,,,Melville,,,,NYNo,,,part,,,of,,,this,,,work,,,may,,,be,,,reproduced,,,,stored,,,in,,,a,,,retrieval,,,system,,,,or,,,transmitted,,,in,,,any,,,form,,,or,,,byany,,,means,,,,electronic,,,,mechanical,,,,photocopying,,,,micro?lming,,,,recording,,,or,,,otherwise,,,,without,,,writtenpermission,,,from,,,the,,,Publisher,,,,with,,,the,,,exception,,,of,,,any,,,material,,,supplied,,,speci?cally,,,for,,,the,,,purposeof,,,being,,,entered,,,and,,,executed,,,on,,,puter,,,system,,,,for,,,exclusive,,,use,,,by,,,the,,,purchaser,,,of,,,the,,,work.Printed,,,on,,,acid-free,,,CharlesUniversityTo,,,our,,,wives,,,and,,,daughtersPreface,,,to,,,the,,,second,,,editionAlmost,,,?fteen,,,years,,,later,,,,and,,,there,,,is,,,little,,,change,,,in,,,our,,,motivation.,,,336,,[OK],,Microeconomics,,Demystified,,[McGraw-Hi.,,>>.,.Adobe,,Flash,,PlayerFlash,,Player,,.,,.pdf,,,18,,,,,,.pdf,,,.pdf,,,.pdf,,,3.pdf,,,,,,,,,.pdf,,,().pdf,,,.pdf,,,.pdf,,,.pdf,,,THE,,,HAAR,,,MEASURE,,,++PDG11,,,+.pdf,,,.pdf,,,,,,Evans.p,,,.pdf,,,.pdf,,,,,,.pdf,,,.pdf,,,,,,.p,,,.pdf,,,.pdf,,,2010.5,,,,,,13.p,,,+1030746,,,ASM,,,Handbook,,,Vol,,,,,,,,,,,,,,,,,,,,,,,,.,,,Hiai,,,,H.,,,,,>,,>,,>Means,,of,,Hilbert,,Space,,Operators,,(F.,,Hilbert,Space,Operators,in,Quan,,,108,0,,,2013-10-31,,Copyright,2008,TheoreticalandMathematicalPhysicsTheseriesfoundedin1975andformerly(until2005)entitledTextsandMonographsinPhysics(TMP)publisheshigh-levelmonographsintheoreticalandmathematicalphysics.ThechangeoftitletoTheoreticalandMathematicalPhysics(TMP)signalsthattheseriesisasuitablepublicationplatformforboththemathematicalandthetheoreticalphysicist.Thewiderscopeoftheseriesisreectedbythecompositionoftheeditorialboard,comprisingbothphysicistsandmathematicians.Thebooks,writteninadidacticstyleandcontainingacertainamountofelementaryback-groundmaterials,bridgethegapbetweenadvancedtextbooksandresearchmonographs.Theycanthusserveasbasisforadvancedstudies,notonlyforlecturesandseminarsatgraduatelevel,butalsoforscientistsenteringaeldofresearch.EditorialBoardW.Beiglbck,InstituteofAppliedMathematics,UniversityofHeidelberg,GermanyJ.-P.Eckmann,DepartmentofTheoreticalPhysics,UniversityofGeneva,SwitzerlandH.Grosse,InstituteofTheoreticalPhysics,UniversityofVienna,AustriaM.Loss,SchoolofMathematics,GeorgiaInstituteofTechnology,Atlanta,GA,USAS.Smirnov,MathematicsSection,UniversityofGeneva,SwitzerlandL.Takhtajan,DepartmentofMathematics,StonyBrookUniversity,NY,USAJ.Yngvason,InstituteofTheoreticalPhysics,UniversityofVienna,AustriaJirBlankPavelExnerMiloslavHavlcekHilbertSpaceOperatorsinQuantumPhysicsSecondEditionABCJirBlankPragueCzechiaPavelExnerDopplerInstituteBrehov711519PragueandNuclearPhysicsInstituteCzechAcademyofSciences25068ReznearPragueCzechRepublicexnerujf.cas.czMiloslavHavlcekDopplerInstituteandFacultyofNuclearSciencesandPhysicalEngineeringCzechTechnicalUniversityTrojanova1312000PragueCzechRepublichavlicekfj.cvut.czISBN978-1-4020-8869-8e-ISBN978-1-4020-8870-4LibraryofCongressControlNumber:2008933703AllRightsReservedc2008SpringerScience+BusinessMediaB.V.c1993,rstedition,AIP,Melville,NYNopartofthisworkmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,microlming,recordingorotherwise,withoutwrittenpermissionfromthePublisher,withtheexceptionofanymaterialsuppliedspecicallyforthepurposeofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthework.Printedonacid-freepaper987654321springer.comCharlesUniversityToourwivesanddaughtersPrefacetothesecondeditionAlmostfteenyearslater,andthereislittlechangeinourmotivation.Mathemat-icalphysicsofquantumsystemsremainsalivelysubjectofintrinsicinterestwithnumerousapplications,bothactualandpotential.Intheprefacetothersteditionwehavedescribedtheoriginofthisbookrootedatthebeginninginacourseoflectures.Withthisfactinmind,wewerenaturallypleasedtolearnthatthevolumewasusedasacoursetextinmanypointsoftheworldandwegladlyacceptedtheoerofSpringerVerlagwhichinheritedtherightsfromouroriginalpublisher,toconsiderpreparationofasecondedition.Itwasourambitiontobringthereaderclosetotheplaceswherereallifedwells,andthereforethiseditionhadtobemorethanacorrectedprinting.Theeldisdevelopingrapidlyandsincethersteditionvariousnewsubjectshaveappeared;asacoupleofexamplesletusmentionquantumcomputingorthemajorprogressintheinvestigationofrandomSchrodingeroperators.Thereare,however,goodsourcesintheliteraturewherethereadercanlearnabouttheseandothernewdevelopments.Wedecidedinsteadtoamendthebookwithresultsaboutnewtopicswhicharelesswellcovered,andthesametime,closertotheresearchinterestsofoneofus.Themainchangeherearetwonewchaptersdevotedtoquantumwaveguidesandquantumgraphs.Followingthespiritofthisbookwehavenotaspiredtofullcoverageeachofthesesubjectswoulddeserveaseparatemonographbutwehavegivenadetailedenoughexpositiontoallowtheinterestedreadertofollow(andenjoy)freshresearchresultsinthisarea.Inconnectionwiththiswehaveupdatedthelistofreferences,notonlyintheaddedchaptersbutalsoinotherpartsofthetextinthesecondpartofthebookwherewefounditappropriate.Naturallywehavecorrectedmisprintsandminorinconsistenciesspottedintherstedition.Wethankthecolleagueswhobroughtthemtoourattention,inparticu-lartoJanaStara,whoindicatednumerousimprovements.Aswiththerstedition,wehaveaskedanativespeakertotrytoremovetheforeignaccentfromourwriting;wearegratefultoMarkHarmerforacceptingthisrole.Prague,December2007PavelExnerMiloslavHavlcekviiPrefaceRelationsbetweenmathematicsandphysicshavealongandentangledtradition.Inspiteofrepeatedclashesresultingfromthedierentaimsandmethodsofthetwodisciplines,bothsideshavealwaysbenetted.Theplacewherecontactsaremostintensiveisusuallycalledmathematicalphysics,orifyouprefer,physicalmathematics.Thesetermsexpressthefactthatmathematicalmethodsareneededheremoretounderstandtheessenceofproblemsthanasacomputationaltool,andconversely,theinvestigatedpropertiesofphysicalsystemsarealsoinspiringfromthemathematicalpointofview.Infact,thiselddoesnotneedanyadvocacy.WhenA.Wightmanremarkedafewyearsagothatithadbecomesociallyacceptable,itwasapleasantunder-statement;byallaccounts,mathematicalphysicsisourishing.Ithaslonglefttheadolescentstagewhenitcherishedonlyoscillatingstringsandmembranes;nowadaysithasbuiltsynapsestoalmosteverypartofphysics.Evidencethatthedisciplineisdevelopingactivelyisprovidedbythefruitfuloscillationbetweentheinvestigationofparticularsystemsandsynthetizinggeneralizations,aswellasbydiscoveriesofnewconnectionsbetweendierentbranches.Thedrawbackofthisrapiddevelopmentisthatithasbecomevirtuallyimpos-sibletowriteatextbookonmathematicalphysicsasasingletopic.Thereare,ofcourse,bookswhichcoverawiderangeofproblems,someofthemindeedmonu-mental,buteventheyarelikecitieswhichgoverntheterritorywhilewatchingthefrontierslowlymovingtowardsthegraydistance.Thisissimplythepricewehavetopayfortheoodofideas,concepts,tools,andresultsthatourscienceisproducing.Itwasnotouraimtowriteapoormansversionofsomeofthebigtextbooks.Whatwewantistogivestudentsbasicinformationabouttheeld,bywhichwemeananamountofknowledgethatcouldconstitutethebasisofanintensiveoneyearcourseforthosewhoalreadyhavethenecessarytraininginalgebraandanalysis,aswellasinclassicalandquantummechanics.Ifourexpositionshouldkindleinterestinthesubject,thestudentwillbeable,aftertakingsuchacourse,toreadspecializedmonographsandresearchpapers,andtodiscoveraresearchtopictohisorhertaste.Wehavementionedthatthespanofthecontemporarymathematicalphysicsisvast;neverthelessthecornerstoneremainswhereitwaslaidbyJ.vonNeumann,H.Weyl,andtheotherfoundingfathers,namelyinregionsconnectedwithquantumtheory.Apartfromitsimportanceforfundamentalproblemssuchastheconstitutionofmatter,thisclaimissupportedbythefactthatquantumtheoryisgraduallyixxPrefacebecomingabasisformostbranchesofappliedphysics,andhasinthiswayenteredoureverydaylife.ThemathematicalbackboneofquantumphysicsisprovidedbythetheoryoflinearoperatorsonHilbertspaces,whichwediscussinthersthalfofthisbook.Herewefollowawelltroddenpath;thisiswhyreferencesinthispartaimmostlyatstandardbooksources,evenforthefewproblemswhichmaybegobeyondthestan-dardcurriculum.Tomaketheexpositionselfcontainedwithoutburdeningthemaintext,wehavecollectedthenecessaryinformationaboutmeasuretheory,integration,andsomealgebraicnotionsintheappendices.Thephysicalchaptersinthesecondhalfarenotintendedtoprovideaselfcontainedexpositionofquantumtheory.Aswehaveremarked,wesupposethatthereaderhasbackgroundknowledgeuptothelevelofastandardquantummechan-icscourse;thepresenttextshouldratherprovidenewinsightsandhelptoreachadeeperunderstanding.However,weattempttodescribethemathematicalfounda-tionsofquantumtheoryinasucientlycompleteway,sothatastudentcomingfrommathematicscanstarthisorherwayintothispartofphysicsthroughourbook.Inconnectionwiththeintendedpurposeofthetext,thecharacterofreferencingchangesinthesecondpart.Thoughthematerialdiscussedhereiswithafewexcep-tionsagainstandard,wetryinthenotestoeachchaptertoexplainextensionsofthediscussedresultsandtheirrelationstootherproblems;occasionallywehavesettrapsforthereaderscuriosity.Thenotesareaccompaniedbyaselectivebutquitebroadlistofreferences,whichmapwaystotheareaswherereallifedwells.Eachchapterisaccompaniedbyalistofproblems.Solvingatleastsomeoftheminfulldetailisthesafestwayforthereadertocheckthatheorshehasindeedmasteredthetopic.Theproblemlevelrangesfromelementaryexercisestofairlycomplicatedproofsandcomputations.Wehaverefrainedfrommarkingthemoredicultoneswithasterisksbecausesuchaclassicationisalwayssubjective,andafterall,inreallifeyoualsooftendonotknowinadvancewhetheritwilltakeyouanhourorhalfayeartodealwithagivenproblem.Letusaddafewwordsaboutthehistoryofthebook.ItoriginatesfromcoursesoflectureswehavegivenindierentformsduringthepasttwodecadesatCharlesUniversityandtheCzechTechnicalUniversityinPrague.Inthe1970swepreparedseveralvolumesoflecturenotes;tenyearslaterwereturnedtothemandrewrotethematerialintoatextbook,againinCzech.Itwaspreparedforpublicationin1989,buttheeconomicturmoilwhichinevitablyaccompaniedthewelcomechangesdelayeditspublication,sothatitappearedonlyrecently.Inthemeantimewesueredaheavyblow.Ourfriendandcoauthor,JirBlank,diedinFebruary1990attheageof50.Hisdepartureremindedusofthebittertruththatweusuallyareabletoappreciatetherealvalueofourrelationshipswithfellowhumansonlyafterwehavelostthem.Hewasalwaysastabilizingelementofourtriumvirateofauthors,andhisspiritasadevotedandpreciseteacherisfeltthroughoutthisbook;wehopethatinthisindirectwayhisclasseswillcontinue.PreparingtheEnglisheditionwasthereforelefttotheremainingtwoauthors.Ithasbeenmodiedinmanyplaces.Firstofall,wehaveincludedtwochaptersandPrefacexisomeothermaterialwhichwaspreparedfortheCzechversionbutthenleftoutduetoeditorialrestrictions.Thoughtheaimofthebookisnottoreportonthepresentstateofresearch,aswehavealreadyremarked,theoriginalmanuscriptwasnishedfouryearsagoandwefeltitwasnecessarytoupdatethetextandreferencesinsomeplaces.Ontheotherhand,sincetheaudienceaddressedbytheEnglishtextisdierentandisequippedwithdierentlibrarieswedecidedtorewritecertainpartsfromthersthalfofthebookinamorecondensedform.Oneconsequenceofthesealterationswasthatwechosetodothetranslationourselves.Thisdecisioncontainedanobviousdanger.Ifyouwriteinalanguagewhichyoudidnotmasterduringyourchildhood,theresultwillnecessarilycontainsomeunwantedcomicaltwistsreminiscentofthefamouscharacterofLeoRosten.WeareindebtedtoP.Moylanand,inparticular,toR.Healey,whohavereadthetextandcounteractedournumerouspettyattacksagainsttheEnglishlanguage;thoseclumsyexpressionsthatremainare,ofcourse,ourown.Therearemanymorepeoplewhodeserveourthanks:coauthorsofourresearchpapers,colleagueswithwhomwehavehadthepleasureofexchangingideas,andsimplyfriendswhohavesupportedusduringdiculttimes.Weshouldnotforgetaboutstudentsinourcourseswhohavehelpedjustbyaskingquestions;someofthemhavenowbecomeourcolleagues.Inviewofthebookcomplexhistory,thelistshouldbeverylong.Weprefertothankallofthemanonymously.However,sinceeveryruleshouldhaveanexception,letusnameJ.Dittrich,whoreadthemanuscriptandcorrectednumerousmistakes.Lastbutnotleastwewanttothankourwives,whosepatienceandunderstandingmadethewritingofthisbookpossible.Prague,July1993PavelExnerMiloslavHavlcekContentsPrefacetothesecondeditionviiPrefaceix1Somenotionsfromfunctionalanalysis11.1Vectorandnormedspaces.11.2Metricandtopologicalspaces.51.3Compactness.101.4Topologicalvectorspaces.131.5Banachspacesandoperatorsonthem.151.6Theprincipleofuniformboundedness.231.7Spectraofclosedlinearoperators.25NotestoChapter1.29Problems.322Hilbertspaces412.1ThegeometryofHilbertspaces.412.2Examples.452.3DirectsumsofHilbertspaces.502.4Tensorproducts.54NotestoChapter2.56Problems.593Boundedoperators633.1Basicnotions.633.2Hermiteanoperators.673.3Unitaryandisometricoperators.723.4Spectraofboundednormaloperators.743.5Compactoperators.773.6HilbertSchmidtandtraceclassoperators.81NotestoChapter3.87Problems.88xiiixivContents4Unboundedoperators934.1Theadjoint.934.2Closedoperators.954.3Normaloperators.Selfadjointness.1004.4Reducibility.Unitaryequivalence.1054.5Tensorproducts.1084.6Quadraticforms.1104.7Selfadjointextensions.1174.8Ordinarydierentialoperators.1264.9Selfadjointextensionsofdierentialoperators.133NotestoChapter4.139Problems.1425Spectraltheory1515.1Projectionvaluedmeasures.1515.2Functionalcalculus.1565.3Thespectraltheorem.1655.4Spectraofselfadjointoperators.1715.5Functionsofselfadjointoperators.1765.6Analyticvectors.1835.7Tensorproducts.1855.8Spectralrepresentation.1875.9Groupsofunitaryoperators.191NotestoChapter5.195Problems.1976Operatorsetsandalgebras2056.1Calgebras.2056.2GNSconstruction.2086.3Walgebras.2136.4NormalstatesonWalgebras.2216.5Commutativesymmetricoperatorsets.2276.6Completesetsofcommutingoperators.2326.7Irreducibility.Functionsofnon-commutingoperators.2356.8Algebrasofunboundedoperators.239NotestoChapter6.241Problems.2467Statesandobservables2517.1Basicpostulates.2517.2Simpleexamples.2597.3Mixedstates.2647.4Superselectionrules.2687.5Compatibility.273Contentsxv7.6Thealgebraicapproach.282NotestoChapter7.285Problems.2898Positionandmomentum2938.1Uncertaintyrelations.2938.2Thecanonicalcommutationrelations.2998.3Theclassicallimitandquantization.306NotestoChapter8.310Problems.3139Timeevolution3179.1Thefundamentalpostulate.3179.2Picturesofmotion.3239.3Twoexamples.3259.4TheFeynmanintegral.3309.5Nonconservativesystems.3349.6Unstablesystems.340NotestoChapter9.348Problems.35410Symmetriesofquantumsystems35710.1Basicnotions.35710.2Someexamples.36210.3Generalspacetimetransformations.,
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