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

Marko Robnik; Valery Romanovski

doi:10.1143/PTPS.139.399

paper

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

arXiv:nlin/0003052 · doi:10.1143/PTPS.139.399

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.

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)

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

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On the semiclassical expansion for 1-dim xN potentials

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