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 oscillator appears as the $\lambda\to 0$ limit of this nonlinear oscillator, whose energy spectrum and eigenfunctions are compared to the linear ones. 
J.F. Cari\~nena, M.F. Ra\~nada and M. Santander