New solutions of relativistic wave equations in magnetic fields and longitudinal fields

We demonstrate how one can describe explicitly the present arbitrariness in solutions of relativistic wave equations in external electromagnetic fields of special form. This arbitrariness is connected to the existence of a transformation, which reduces eff

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aNewsolutionsofrelativisticlongitudinalwaveequations elds.inmagnetic eldsandV.G.Bagrov ,M.C.Baldiotti ,D.M.Gitman ,andI.V.Shirokov§InstitutodeF´ sica,UniversidadedeS aoPaulo,C.P.66318,05315-970S aoPaulo,SP,Brasil(February1,2008)AbstractWedemonstratehowonecandescribeexplicitlythepresentarbitrarinessinsolutionsofrelativisticwaveequationsinexternalelectromagnetic eldsofspecialform.Thisarbitrarinessisconnectedtotheexistenceofatransforma-tion,whichreducese ectivelythenumberofvariablesintheinitialequations.Thenweusethecorrespondingrepresentationstoconstructnewsetsofex-actsolutions,ly,wepresentnewsetsofstationaryandnonstationarysolutionsinmagnetic eldandinsomesuperpositionsofelectricandmagnetic elds.I.INTRODUCTIONRelativisticwaveequations(DiracandKlein-Gordon)provideabasisforrelativisticquantummechanicsandquantumelectrodynamicsofspinorandscalarparticles[1].Inrelativisticquantummechanics,solutionsofrelativisticwaveequationsarereferredtoasone-particlewavefunctionsoffermionsandbosonsinexternalelectromagnetic elds.Inquantumelectrodynamics,suchsolutionsallowthedevelopmentoftheperturbationexpansionknownastheFurrypicture,whichincorporatestheinteractionwiththeexternal eldexactly,

whiletreatingtheinteractionwiththequantizedelectromagnetic eldperturbatively[2].ThephysicallymostimportantexactsolutionsoftheKlein-GordonandtheDiracequationsare:anelectroninaCoulomb eld,auniformmagnetic eld,the eldofaplanewave,the eldofamagneticmonopole,the eldofaplanewavecombinedwithauniformmagneticandelectric eldsparalleltothedirectionofwavepropagation,crossed elds,andsome

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