Self-interacting one-dimensional oscillators

摘要

Energy eigenvalues and < x~2 >_n for the oscillators having potential energy V(x) = (ω~2x~2/2) + λ < x~(2r) > x~(2s) have been determined for various values of λ, r, s and n using renormalized hypervirial-Pade scheme. In general, the results show an improvement over the findings of earlier workers. Variation of the evaluated quantities and of the renormalization parameter with λ, r, s and n has been discussed. In addition, this potential has been employed as an illustrative example of the applicability of alternative formalism of perturbation theory developed by Kim and Sukhatme (J. Phys. A25 647 (1992)).