SOME POLYNOMIAL PERTURBATION PROBLEMS AND THE ROTATING DISPLACED OSCILLATOR

Interesting coincidences in the energy spectra of the binding potentials V+/- = -/+a/r+/-br+cr2, rooted in the invariance of the kinetic energy operator under a discrete coordinate transformation, are pointed out. The discontinuous behavior of exact energy eigenvalues under a permitted variation of the coupling parameters is linked to the disappearance of the associated normalized wavefunctions in the limits envisaged. A set of exact solutions of the rotating displaced oscillator problem for arbitrary angular momentum values is also recorded.