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Exact Solutions of Schrodinger Equation for the Position-Dependent Effective Mass Harmonic Oscillator

Naila, Amir, Shahid, Iqbal

Published Jan 1, 2014• 0 citations

Abstract

A one-dimensional harmonic oscillator with position-dependent effective mass is studied. We quantize the oscillator to obtain a quantum Hamiltonian, which is manifestly Hermitian in configuration space, and the exact solutions to the corresponding Schr¨odinger equation are obtained analytically in terms of modified Hermite polynomials.It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the position dependence of the mass vanishes.

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