IJPAM: Volume 37, No. 4 (2007)
THE TIME-DEPENDENT SCHRÖDINGER EQUATION
Department of Science
University of Colima
Bernal Diaz del Castillo 340, Col. Villas San Sebastian
Colima, Col., C.P. 28045, MEXICO
e-mail: [email protected]
Abstract.We consider fractional Darboux transformations (FDT), recently defined for the stationary Schrödinger equation,
and generalize them to a certain class of
time-dependent Schrödinger equations (TDSE). The FDT is related to the well known
Darboux transformation, but none of both transformations is a special case of the other one. We state the transformed
solution of the TDSE and its transformed potential is closed form. Our results are finally generalized to TDSEs
steming from Hamiltonians with linear terms in the momentum.
Received: March 11, 2007
AMS Subject Classification: 46N50
Key Words and Phrases: fractional Darboux transformation, time-dependent Schrödinger equation
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 37
Issue: 4
