First-order Intertwining Operators and Position-dependent Mass Schrödinger Equations in d Dimensions

The problem of d-dimensional Schrödinger equations with a position-dependent mass is analyzed in the framework of first-order intertwining operators. With the pair (H,H1) of intertwined Hamiltonians one can associate another pair of secondorder partial differential operators (R,R1), related to the same intertwining operator and such that H (resp. H1) commutes with R (resp. R1). 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 Schrödinger equation or that of H and R together with SUSYQM and shape-invariance techniques. The relation between both approaches is also studied. PACS: 03.65.-w