Quantum Mechanics for Mathematicians.pdf

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1、QuantumMechanicsforMathematiciansLeonA.TakhtajanGraduateStudiesinMathematicsVolume95AmericanMathematicalSocietyProvidence,RhodeIslandEditorialBoardDavidCox(Chair)StevenG.KrantzRafeMazzeoMartinScharlemann2000MathematicsSubjectClassification.Primary81-01.Foradditionalinformationandup

2、datesonthisbook,visitwww.ams.org/bookpages/gsm-95LibraryofCongressCataloging-in-PublicationDataTakhtadzhian,L.A.(LeonArmenovich)Quantummechanicsformathematicians/LeonA.Takhtajan.p.cm.-(Graduatestudiesinmathematics;v.95)Includesbibliographicalreferencesandindex.ISBN978-0-8218-4630-8

3、(alk.paper)1.Quantumtheory.2.Mathematicalphysics.I.Title.QC174.12.T3432008530.12-dc222008013072Copyingandreprinting.Individualreadersofthispublication,andnonprofitlibrariesactingforthem,arepermittedtomakefairuseofthematerial,suchastocopyachapterforuseinteachingorresearch.Permission

4、isgrantedtoquotebriefpassagesfromthispublicationinreviews,providedthecustomaryacknowledgmentofthesourceisgiven.Republication,systematiccopying,ormultiplereproductionofanymaterialinthispublicationispermittedonlyunderlicensefromtheAmericanMathematicalSociety.Requestsforsuchpermission

5、shouldbeaddressedtotheAcquisitionsDepartment,AmericanMathematicalSociety,201CharlesStreet,Providence,RhodeIsland02904-2294,USA.Requestscanalsobemadebye-mailtoreprint-permission@ams.org.©2008bytheAmericanMathematicalSociety.Allrightsreserved.TheAmericanMathematicalSocietyretainsallr

6、ightsexceptthosegrantedtotheUnitedStatesGovernment.PrintedintheUnitedStatesofAmerica.®Thepaperusedinthisbookisacid-freeandfallswithintheguidelinesestablishedtoensurepermanenceanddurability.VisittheAMShomepageathttp://ww.ams.org/10987654321131211100908TomyteacherLudwigDmitrievichFad

7、deevwithadmirationandgratitude.ContentsPrefacePart1.FoundationsChapter1.ClassicalMechanics§1.LagrangianMechanics1.1.Generalizedcoordinates1.2.Theprincipleoftheleastaction1.3.ExamplesofLagrangiansystems1.4.SymmetriesandNoether'stheorem1.5.One-dimensionalmotion1.6.Themotioninacentral

8、fieldandtheKeplerproblem1.