arXiv math-ph/05060172005-06math-phhep-thmath.MPquant-ph

Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation

A Kamenshchik, M Luzzi, G Venturi

备注：: The collective of the authors is enlarged and the calculations in Sec. 3 are corrected
发表信息：: Russ.Phys.J.52:1339-1351,2009
DOI：: 10.1007/s11182-010-9375-4

英文摘要：

The connection between the method of comparison equations (generalized WKB method) and the Ermakov-Pinney equation is established. A perturbative scheme of solution of the generalized Ermakov-Pinney equation is developed and is applied to the construction of perturbative series for second-order differential equations with and without turning points.

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