One-dimensional model of a quantum nonlinear harmonic oscillator
J. F. Cariñena, M. F. Rañada, M. Santander
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 0 limit of this nonlinear oscillator, whose energy spectrum and eigenfunctions are compared to the linear ones.
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