Flatland Position-Dependent-Mass: Polar Coordinates, Separability and Exact Solvability
S. Habib Mazharimousavi, Omar Mustafa
TL;DR
This paper derives the kinetic energy operator for position-dependent mass in polar coordinates, discusses Schrödinger equation separability, and presents exactly solvable models to illustrate the approach.
Contribution
It introduces a new form of the kinetic energy operator in polar coordinates for position-dependent mass systems and provides exactly solvable examples.
Findings
Derived the kinetic energy operator in polar coordinates for PDM systems
Analyzed the separability of the Schrödinger equation in this context
Presented two exactly solvable models
Abstract
The kinetic energy operator with position-dependent-mass in plane polar coordinates is obtained. The separability of the corresponding Schr\"odinger equation is discussed. A hypothetical toy model is reported and two exactly solvable examples are studied.
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