Some properties of WKB series
نویسندگان
چکیده
We investigate some properties of the WKB series for arbitrary analytic potentials and then specifically for potentials x (N even), where more explicit formulae for the WKB terms are derived. Our main new results are: (i) We find the explicit functional form for the general WKB terms σ k, where one has only to solve a general recursion relation for the rational coefficients. (ii) We give a systematic algorithm for a dramatic simplification of the integrated WKB terms ∮ σ kdx that enter the energy eigenvalue equation. (iii) We derive almost explicit formulae for the WKB terms for the energy eigenvalues of the homogeneous power law potentials V (x) = x , where N is even. In particular, we obtain effective algorithms to compute and reduce the terms of these series. PACS numbers: 03.65.-w, 03.65.Ge, 03.65.Sq Submitted to Journal of Physics A: Mathematical and General e–mail: [email protected] e–mail: [email protected] 1
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