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1、REVIEWSOFMODERNPHYSICS,VOLUME82,JULY–SEPTEMBER2010NormalizationandglobalanalysisofperturbationsofthehydrogenatomK.Efstathiou*DepartmentofMathematics,UniversityofGroningen,Groningen9700AK,TheNetherlands†D.A.SadovskiíDépartementdePhysique,UniversitéduLi
2、ttoral–Côted’Opale,59140Dunkerque,FrancePublished3August2010ThehydrogenatomperturbedbysufÞcientlysmallhomogeneousstaticelectricandmagneticÞeldsofarbitrarymutualalignmentisaspeciÞcperturbationoftheKeplersystemwiththreedegreesoffreedomandthreeparamete
3、rs.NormalizationoftheKepleriansymmetryrevealsthattheparameterspaceisstratiÞedintoresonantzonesofsystems,eachzonewithaninternaldynamicalstratiÞcationofitsownEfstathiou,Sadovski,andZhilinski,2007,Proc.R.Soc.London,Ser.A463,1771.Basedonthefullyintegrab
4、leapproximation,thebundleofinvarianttoriofindividualsystemswithinzonesischaracterizedgloballyandthequalitativedynamicalstratiÞcationisuncovered.Thetechniquesinvolvedinthisanalysisareillustratedwiththeexampleofthe1:1resonancezonenearorthogonalÞeldswh
5、osestructureisknownatpresent.Applicationsinthecorrespondingquantumsystemarealsodescribed.DOI:10.1103/RevModPhys.82.2099PACSnumbers:32.60.i,03.65.Vf,45.05.x,03.65.SqCONTENTS4.Generalizedorfractionalmonodromy21105.Monodromymapanditsmatrix2111E.Quant
6、um-classicalcorrespondence2111I.Introduction21001.Quantumjointspectrumlattice2111A.Globaldynamicalanalysis21002.Quantummonodromy21121.Characteristicsofindividualperturbations21003.Generalizations21122.StratiÞcationoftheparameterspace2101F.Mainconjectu
7、reoftheglobalclassiÞcation2112B.Hamiltonianandparameterspace21011.ToricÞbrationsandtheirBD2112C.Historicaloverviewandperspective21022.RecoveringtopologyofsingularÞbrationsD.Structureofthepaper2102fromtheirBD2113II.BasicMathematicalConcepts21033.Extend
8、ingtosystemswithhyperbolicA.Regularization,Þrstintegrals,andtheirßows2103singularÞbers2113B.Geometryofthereductionmap21034.Extendingtonearlyintegrablesystems21131.FirstorKeplerianreduction2103III.Results:QualitativeTypesofPerturbations21132.Re
