On the Semiclassical Expansion for 1-DimxNPotentials | Zendy

Marko Robnik | Zendy; Valery G. Romanovski | Zendy

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On the Semiclassical Expansion for 1-Dimx^NPotentials

Author(s) -

Marko Robnik,

Valery G. Romanovski

Publication year - 2000

Publication title -

progress of theoretical physics supplement

Language(s) - English

Resource type - Journals

ISSN - 0375-9687

DOI - 10.1143/ptps.139.399

Subject(s) - wkb approximation , semiclassical physics , eigenvalues and eigenvectors , polynomial , simple (philosophy) , series (stratigraphy) , mathematical physics , physics , quantum mechanics , energy (signal processing) , mathematics , mathematical analysis , quantum , paleontology , philosophy , epistemology , biology

In the present paper we study the structure of the WKB series for thepolynomial potential $V(x)=x^N$ ($N$ even). In particular, we obtain relativelysimple recurrence formula of the coefficients $\s'_k$ of the semiclassicalapproximation 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

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