First-order intertwining operators and position-dependent mass Schrodinger equations in d dimensions

摘要

The problem of d-dimensional Schrodinger equations with a position-dependent mass is analyzed in the framework of first-order intertwining operators. With the pair (H,H-1) of intertwined Hamiltonians one can associate another pair of second-order partial differential operators (R,R,), related to the same intertwining operator and such that H (resp. H-1) commutes with R (resp. R-1). This property is interpreted in superalgebraic terms in the context of supersymmetric quantum mechanics (SUSYQM). In the two-dimensional case, a solution to the resulting system of partial differential equations is obtained and used to build a physically relevant model depicting a particle moving in a semi-infinite layer. Such a model is solved by employing either the commutativity of H with some second-order partial differential operator L and the resulting separability of the Schrodinger equation or that of H and R together with SUSYQM and shape-invariance techniques. The relation between both approaches is also studied. (c) 2005 Elsevier Inc. All rights reserved.