A new approach to determination of the energy levels of the bound states in quantum mechanics. Convergent perturbation theory
A perturbation theory (PT), each term of which is expressed in quadratures, is constructed. A procedure for selecting the zeroth approximation, which leads to a fast convergence of the PT series is formulated. As an example, the ground and first-excited states in the potential V(x) = x2n (n — 2, 3, 4) are calculated.