A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog

Details A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog

2007-02-24

arxiv.org/abs/math-ph/0702084v1

SIGMA 3 (2007), 030, 23 pages

Physics

Mathematical Physics

This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portuga

Scientific paper

10.3842/SIGMA.2007.030

Two super-integrable and super-separable classical systems which can be considered as deformations of the harmonic oscillator and the Smorodinsky-Winternitz in two dimensions are studied and identified with motions in spaces of constant curvature, the deformation parameter being related with the curvature. In this sense these systems are to be considered as a harmonic oscillator and a Smorodinsky-Winternitz system in such bi-dimensional spaces of constant curvature. The quantization of the first system will be carried out and it is shown that it is super-solvable in the sense that the Schr\"odinger equation reduces, in three different coordinate systems, to two separate equations involving only one degree of freedom.

Affiliated with

Also associated with

No associations

Rating

A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-582346