One-dimensional model of a quantum nonlinear harmonic oscillator

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 osci...

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Bibliographic Details
Published in:Reports on mathematical physics 2004-10, Vol.54 (2), p.285-293
Main Authors: Cariñena, José F., Rañada, Manuel F., Santander, Mariano
Format: Article
Language:English
Subjects:
exactly solvable systems
Nonlinear oscillator
position-dependent mass
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Summary: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.
ISSN:0034-4877
1879-0674
DOI:10.1016/S0034-4877(04)80020-X