Quantum Hamilton-Jacobi Approach to Two Dimensional Singular Oscillator

TL;DR

This paper applies the quantum Hamilton-Jacobi formalism to solve the two-dimensional singular oscillator, deriving eigenfunctions, solvability conditions, and generating new potentials based on initial states.

Contribution

It introduces a novel application of the quantum Hamilton-Jacobi approach to the 2D singular oscillator, providing new solutions and potential generation methods.

Findings

Eigenfunctions and solvability conditions derived

New potentials generated from initial states

Solutions obtained in both Cartesian and parabolic coordinates

Abstract

We have obtained the solutions of two dimensional singular oscillator which is known as the quantum Calogero-Sutherland model both in cartesian and parabolic coordinates within the framework of quantum Hamilton Jacobi formalism. Solvability conditions and eigenfunctions are obtained by using the singularity structures of quantum momentum functions under some conditions. New potentials are generated by using the first two states of singular oscillator for parabolic coordinates.