One-dimensional model of a quantum nonlinear harmonic oscillator

Abstract

In this paper we study the quantization of the nonlinear oscillator introduced by Mathews and Lakshmanan. This system with position-dependent mass allows a natural quantization procedure and is shown to display shape invariance. Its energy spectrum is found by factorization. The linear harmonic oscillator appears as the $\lambda \to 0$ limit of this nonlinear oscillator, whose energy spectrum and eigenfunctions are compared to the linear ones.

References in corpus (2)

• A non-linear Oscillator with quasi-Harmonic behaviour: two- and $n$-dimensional Oscillators
• A systematic study on the exact solution of the position dependent mass Schroedinger equation

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