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时间:2019-03-06
《Neumaier--Classical & Quantum Mechanics via Lie Algebras 2011.pdf》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、ClassicalandquantummechanicsviaLiealgebrasArnoldNeumaierDennisWestraUniversityofVienna,AustriaApril14,2011Thisisthedraftofabook.Themanuscripthasnotyetfullbookquality.Pleaserefertothebookonceitispublished.Untilthen,we’dappreciatesuggestionsforimprovement
2、s;pleasesendthemtoArnold.Neumaier@univie.ac.atcopyrightcbyArnoldNeumaierandDennisWestraContentsPrefaceixIAninvitationtoquantummechanics11Motivation31.1Classicalmechanics................................31.2Relativitytheory................................
3、.51.3Statisticalmechanicsandthermodynamics...................71.4Hamiltonianmechanics..............................81.5Quantummechanics...............................101.6Quantumfieldtheory...............................131.7TheSchr¨odingerpicture.......
4、......................131.8TheHeisenbergpicture..............................151.9Outlineofthebook................................172Thesimplestquantumsystem252.1Matrices,relativityandquantumtheory....................262.2Continuousmotionsandmatrixgroup
5、s.....................282.3InfinitesimalmotionsandmatrixLiealgebras.................292.4Uniformmotionsandthematrixexponential..................312.5Volumepreservationandspeciallineargroups.................332.6Thevectorproduct,quaternions,andSL(2,C)....
6、.............35iiiCONTENTS2.7TheHamiltonianformofaLiealgebra.....................382.8Atomicenergylevelsandunitarygroups....................392.9QubitsandBlochsphere.............................402.10Polarizedlightandbeamtransformations.................
7、...412.11Spinandspincoherentstates..........................442.12Particlesanddetectionprobabilities.......................472.13Photonsondemand................................482.14UnitaryrepresentationsofSU(2)........................533Thesymmetriesof
8、theuniverse573.1RotationsandSO(n)...............................573.23-dimensionalrotationsandSO(3).......................603.3Rotationsandquaternions............................633.4RotationsandSU(2).............................
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