Strong coupling perturbation expansions for anharmonic oscillators. Numerical results

The strong coupling expansion coefficients for the ordinary and renormalize d energies of the ground and first excited states of the quartic, sextic, o ctic and decadic anharmonic oscillators with the Hamiltonian H = p(2) + x(2 ) + beta x(2m), m = 2, 3, 4, 5 are computed. The expansion coefficients are also computed for higher excited states of the quartic oscillator. The lar ge-order behaviour of the coefficients, the radii of convergence of the ser ies and the summation rules for the coefficients are discussed. It is shown that, in contrast to the divergent weak coupling expansions, the renormali zed strong coupling perturbation wavefunctions have simple form and straigh tforward physical interpretation. Finally, both the strong coupling perturb ation approaches are compared.