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Journal of Physical Studies 16(1/2), Article 1003 [10 pages] (2012)
DOI: https://doi.org/10.30970/jps.16.1003 QUASI-EXACTLY SOLVABLE POTENTIALS FOR A PARTICLE WITH A POSITION-DEPENDENT MASSO. Voznyak, V. M. Tkachuk
Department for Theoretical Physics, Ivan Franko National University of Lviv, |
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The method of supersymmetric quantum mechanics for generating quasi-exactly solvable potentials has been extended for the case of systems with a position-dependent mass. The exact solutions for the ground and first excited state have been found when both superpotential and position-dependent mass are generating functions. The conditions for the existence of the ground and first excited state for different behaviors of the position-dependent mass in the same potential, as well as those of existence of the bounded states in the case of constant potential and coordinate dependent mass have been studied. Numerous examples have been provided.
PACS number(s): 03.65.-w, 11.30.Pb