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One-dimensional model of a quantum nonlinear harmonic oscillator

2004
9 pages
Published in:
  • Rept.Math.Phys. 54 (2004) 285
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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→0\lambda\to 0 limit of this nonlinear oscillator, whose energy spectrum and eigenfunctions are compared to the linear ones.
  • NONLINEAR OSCILLATOR
  • POSITION-DEPENDENT MASS
  • EXACTLY SOLVABLE SYSTEMS