Knowledge Bank

The perturbation formalism developed by $Louck1$ has been applied to the quantum mechanical simple harmonic oscillator perturbed by polynomial terms in the displacement coordinate q. The method leads to general expressions to all orders of approximation for the perturbed energies and eigenfunctions, and does not require numerical calculation for each unperturbed state separately. Exact calculations to third and fourth order are possible for polynomials of lower degree, and approximate expressions can be obtained for polynomials of higher degree and for higher orders of approximation.