Analytic approximants for the energy eigenvalues of anharmonic potentials

A technique is presented that allows to obtain analytic approximations for the energy eigenvalues of the one-dimensional Schrodinger equation with anharmonic potentials. This technique is based on an original way of obtaining perturbative expansions, together with the used of quasi-rational approximants found from these expansions at various points. The technique is applied explicitly to the ground state of the quartic anharmonic oscillator.