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The energy eigenvalues of the anharmonic oscillator characterized by the cubic potential for various eigenstates are determined within the framework of the hypervirial-Pade summation method. For this purpose the E[3,3] and E[3,4] Pade approximants are formed to the energy perturbation series and given the energy eigenvalues up to fourth order in terms of the anharmonicity parameter $lambda$.
It is shown that for the one-dimensional quantum anharmonic oscillator with potential $V(x)= x^2+g^2 x^4$ the Perturbation Theory (PT) in powers of $g^2$ (weak coupling regime) and the semiclassical expansion in powers of $hbar$ for energies coincide
We outline a remarkably efficient method for generating solutions to quantum anharmonic oscillators with an x^{2M} potential. We solve the Schroedinger equation in terms of a free parameter which is then tuned to give the correct boundary condition b
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the $hbar$-expansions and suitable quantization conditions a new procedure for de
A simple method for the calculation of higher orders of the logarithmic perturbation theory for bound states of the spherical anharmonic oscillator is developed. The structure of the perturbation series for energy eigenvalues of the sextic doubly anh
The spectral problem for O(D) symmetric polynomial potentials allows for a partial algebraic solution after analytical continuation to negative even dimensions D. This fact is closely related to the disappearance of the factorial growth of large orde