On the semiclassical expansion for 1-dim $x^N$ potentials

Abstract

In the present paper we study the structure of the WKB series for the polynomial potential $V(x)=x^N$ ($N$ even). In particular, we obtain relatively simple recurrence formula of the coefficients \s'_k of the semiclassical approximation and of the WKB terms for the energy eigenvalues.Comment: 5 pages, PTP LaTeX style, to be published in the proceedings of the conference/summer school 'Let's Face Chaos through Nonlinear Dynamics', Maribor, Slovenia, June/July 1999, eds. M. Robnik et al., Prog. Theor. Phys. Suppl. (Kyoto) 139 (2000