Indian Journal of Physics

, Volume 92, Issue 3, pp 357–367 | Cite as

Exact analytic solution of position-dependent mass Schrödinger equation

Original Paper
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Abstract

Exact analytic solution of position-dependent mass Schrödinger equation is generated by using extended transformation, a method of mapping a known system into a new system equipped with energy eigenvalues and corresponding wave functions. First order transformation is performed on D-dimensional radial Schrödinger equation with constant mass by taking trigonometric Pöschl–Teller potential as known system. The exactly solvable potentials with position-dependent mass generated for different choices of mass functions through first order transformation are also taken as known systems in the second order transformation performed on D-dimensional radial position-dependent mass Schrödinger equation. The solutions are fitted for “Zhu and Kroemer” ordering of ambiguity. All the wave functions corresponding to nonzero energy eigenvalues are normalizable. The new findings are that the normalizability condition of the wave functions remains independent of mass functions, and some of the generated potentials show a family relationship among themselves where power law potentials also get related to non-power law potentials and vice versa through the transformation.

Keywords

Position-dependent mass Pöschl–Teller potential Exact analytic solution Exactly solvable potential Extended transformation 

PACS Nos.

03.65.Ge 03.65.Db 

Notes

Acknowledgements

The author is indebted to (late) professor S. A. S. Ahmed, Gauhati University, Gwahati, India who helped with valuable suggestions at the early stage of the work.

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Copyright information

© Indian Association for the Cultivation of Science 2017

Authors and Affiliations

  1. 1.Physics DepartmentNalbari CollegeNalbariIndia

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