The Lennard-Jones oscillator in quantum Hamilton-Jacobi theory

We present a new scheme for calculating the energy eigenvalues of an oscillator modeled using the Lennard-Jones (12,6) potential for the zero angular momentum case. The eigenvalues are calculated using the quantum Hamilton-Jacobi theory making use of the action variable without obtaining a full solution of the dynamical equation. The energy eigenvalues so obtained are compared with those calculated numerically.