Strong coupling perturbation expansions for anharmonic oscillators.: Numerical results

The strong coupling expansion coefficients for the ordinary and renormalized energies of the ground and first excited states of the quartic, sextic, octic 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 large-order behaviour of the coefficients, the radii of convergence of the series and the summation rules for the coefficients are discussed. It is shown that, in contrast to the divergent weak coupling expansions, the renormalized strong coupling perturbation wavefunctions have simple form and straightforward physical interpretation. Finally, both the strong coupling perturbation approaches are compared.