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1、EffectiveMassSchr¨odingerEquationforExactlySolvableClassofOne-DimensionalPotentialsMetinAkta¸sa,RamazanSeverb∗aDepartmentofPhysics,FacultyofArtsandSciencesKırıkkaleUniversity,71450,Kırıkkale,TurkeybDepartmentofPhysics,MiddleEastTechnicalUniversity06531Ankara,TurkeyFebruary1,2008Abstrac
2、tWedealwiththeexactsolutionsofSchr¨odingerequationcharacterizedbyposition-dependenteffectivemassviapointcanonicaltransformations.TheMorse,P¨oschl-TellerandHulth´entypepotentialsareconsideredrespectively.Withthechoiceofposition-dependentmassforms,exactlysolvabletargetpotentialsareconstr
3、ucted.Theirenergyoftheboundstatesandcorrespondingwavefunctionsaredeterminedexactly.PACSnumbers:03.65.-w;03.65.Ge;12.39.FdKeywords:Position-dependentmass,Pointcanonicaltransformation,EffectivemassSchr¨odingerequation,Morsepotential,P¨oschl-Tellerpotential,Hulth´enpotential.arXiv:quant-p
4、h/0608054v17Aug2006∗Correspondingauthor:E-mail:sever@metu.edu.tr11IntroductionTherehasrecentlybeenacontinualinteresttothesolutionsofSchr¨odingerequationsde-scribingsystemswithspatiallydependenteffectivemasses[1-11].Systemswithcertaintypesofeffectivemassesarefoundtobeusefulinthedetermina
5、tionofphysicalproper-tiesofsemiconductorheterostructures[12],quantumliquidsanddots[13,14],heliumandmetaltypeclusters[15,16]andnuclei[17]aswell.Inadditiontothese,thequantummechanicsforsystemsofparticlewithsometypesofmasseshasnotonlybeenconsideredfortheinstantaneousGalileaninvariance[18
6、],butalsostudiedforthepathintegralap-proach[19]andsu(1,1)Liealgebraictechniqueetc.[20,21].Nomatterhowdifficultexactsolutionsofaretoobtain,theeffectivemassSchr¨odingerequationforcertaintypepoten-tialscanbesolved[22,23].WithintheframeworkofSUSYQM,problemsincludingtheshapeinvariancerequirem
7、entaresolvedexactly[24-27].InthemappingofthenonconstantmassSchr¨odingerequation,pointcanonicaltransformations(PCTs)areemployed[28-31].Whendealingwiththisprocess,weneedtotransformittoaconstantmassonesothatthelatterequationcanbesolvedeasily.Therefore,itwillyieldboththeenergyspectraandco
8、rresp
