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arXiv:1003.3003 · Symmetry Integrability and Geometry Methods and Applications

Flatland Position-Dependent-Mass: Polar Coordinates, Separability and Exact Solvability

S. Habib Mazharimousavi

Published Oct 29, 2010• 2 citations
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Abstract

The kinetic energy operator with position-dependent-mass in plane polar coordinates is obtained.The separability of the corresponding Schrödinger equation is discussed.A hypothetical toy model is reported and two exactly solvable examples are studied.
DOI
10.3842/sigma.2010.088

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This communication has been dedicated to quantum dynamics of particle whose mass depends on coordinate. We considered one dimensional model which admits to obtain the exact solution of wave equation. The position dependent mass was represented as the periodic function. Inside of period the mass varies accordingly to the inverse proportionality. We have found wave functions in their explicit form as well as energy eiguen values. It has been shown that the energy spectrum manifests properties typical for periodic nanostructures.
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