Quantum Hamilton--Jacobi Approach to Two Dimensional Singular Oscillator

We obtain 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.