Abstract. We present a new method for the solution of the Schrödinger equation applicable to problems of a non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: an asymptotic scale, which depends uniquely on the form of the potential at large distances; an intermediate scale, still characterized by an exponential decay of the wavefunction; and, finally, a short distance scale, in which the wavefunction is sizable. The notion of optimized perturbation is then used in the last two regimes. We apply the method to the quantum anharmonic oscillator and find it suitable to treat both energy eigenvalues and wavefunctions, even for strong couplings.

PACS numbers: 03.65.Ge, 02.30.Mv, 11.15.Bt, 11.15.Tk

Print publication: Issue 10 (12 March 2004)
Received 3 November 2003
Published 24 February 2004