Eur. Phys. J. Plus (2013) 128: 54
https://doi.org/10.1140/epjp/i2013-13054-8

Regular Article

Higher-dimensional realization of a nonlinear, one-parameter quantum oscillator

¹³⁴⁵ Department of Mathematics and Actuarial Science and Department of Physics, Indiana University Northwest, 46408, Gary, IN, USA
²³⁴⁵ Department of Physics, Indiana University Northwest, 3400 Broadway, 46408, Gary, IN, USA

^* e-mail: axgeschu@iun.edu

Received: 23 February 2013
Revised: 8 May 2013
Accepted: 9 May 2013
Published online: 27 May 2013

Abstract

We generalize a recently introduced quantum model of a nonlinear oscillator to arbitrary dimensions. In our realization of the model we impose hyperspherical symmetry, which allows for separation of variables in the governing equation. We obtain the discrete spectrum in closed form, as well as the corresponding orthogonal set of normalizable eigenfunctions, located in a weighted Hilbert space. Furthermore, conditions for emptiness of the discrete spectrum are obtained, as well as spectral bounds for the eigenvalues.