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SIGMA 3 (2007), 067, 14 pages arXiv:0705.2577
https://doi.org/10.3842/SIGMA.2007.067
Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions
Christiane Quesne
Physique Nucléaire Théorique et Physique Mathématique, Université Libre de
Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels, Belgium
Received March 30, 2007, in final form May 08, 2007; Published online May 17, 2007
Abstract
An exactly solvable position-dependent mass Schrödinger equation in two dimensions,
depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories
describing superintegrable two-dimensional systems with integrals of motion that are quadratic
functions of the momenta. To get the energy spectrum a quadratic algebra approach is used together
with a realization in terms of deformed parafermionic oscillator operators. In this process, the
importance of supplementing algebraic considerations with a proper treatment of boundary conditions
for selecting physical wavefunctions is stressed. Some new results for matrix elements are derived.
This example emphasizes the interest of a quadratic algebra approach to position-dependent mass
Schrödinger equations.
Key words:
Schrödinger equation; position-dependent mass; quadratic algebra.
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