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

Nonlinear Sciences – Chaotic Dynamics

Scientific paper

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5 pages, PTP LaTeX style, to be published in the proceedings of the conference/summer school 'Let's Face Chaos through Nonline

Scientific paper

10.1143/PTPS.139.399

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.

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