Some Properties of a Quartic Potential with a Finite Binding Energy

A potential energy function is proposed which exhibits a quartic dependence on (r - re), where re is the equilibrium interparticle distance, in the neighbourhood of re, and has a finite binding energy. To study the pattern of the eigenvalues, the WKBJ method is applied to the third order, and the relevant integrals are evaluated analytically. Results are shown graphically for a few sets of parameters. The number of vibrational states that the potential can support is determined for a range of values of the parameters. Some suggestions as to the possible applications of the proposed potential are also made.