Neumaier--Classical &ampamp;amp; Quantum Mechanics via Lie Algebras 2011.pdf

《Neumaier--Classical &ampamp;amp; 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).............................