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arXiv · hep-th/0501106

One-dimensional model of a quantum nonlinear harmonic oscillator

J. F. Cariñena·M. F. Rañada·M. Santander
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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 $λ\to 0$ limit of this nonlinear oscillator, whose energy spectrum and eigenfunctions are compared to the linear ones.

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J. F. Cariñena, M. F. Rañada, M. Santander. 2005-01-14. One-dimensional model of a quantum nonlinear harmonic oscillator. https://doi.org/10.1016/s0034-4877(04)80020-x

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