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Quasi-Exactly Solvable Time-Dependent Potentials

We find exact solutions of the time-dependent Schr\"odinger equation for a family of quasi-exactly solvable time-dependent potentials by means of non-unitary gauge transformations.

Quasi-ExactlySolvableTime-DependentPotentials

arXiv:physics/9705022v1 17 May 1997FedericoFinkel( )DepartamentodeF´ sicaTe´oricaIIUniversidadComplutenseMadrid28040SPAINNikyKamran( )TheFieldsInstituteforResearchintheMathematicalSciences222CollegeStreetToronto,Ontario,M5T3J1CANADAAbstractWe ndexactsolutionsofthetime-dependentSchr¨odingerequationforafamilyofquasi-exactlysolvabletime-dependentpotentialsbymeansofnon-unitarygaugetransformations.PACSnumbers:03.65.Ge,11.30.Na,03.65.Fd

( )ResearchsupportedbyDCGICYTGrant#PB95-0401.

( )ResearchsupportedbyNSERCGrant#0GP0105490,onsabbaticalleavefromtheDepartmentofMathematicsandStatistics,McGillUniversity,Montr´eal,Qu´ebec,H3A2K6,Canada.

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