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

par Quesne, Christiane
Référence Annals of physics, 321, 5, page (1221-1239)
Publication Publié, 2006-05

Article révisé par les pairs

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Résumé :

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 second-order 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. © 2005 Elsevier Inc. All rights reserved.