Analytic solution of the general anharmonic-oscillator problem期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Analytic solution of the general anharmonic-oscillator problem

Authors:	M. Znojil

Affiliation:	(1) Nuclear Physics Institute, Czechoslovak Academy of Sciences, 250 68 e near, Prague, Czechoslovakia

Abstract:	The regular and irregular solution of the differential three-dimensional Schrödinger equation with the confining potential $V(r) = g_{ - 2} r^{ - 2} + g_{ - 1} r^{ - 1} + g_1 r + ... + g_{2q} r^{2q} ,q geqslant 1$ , is presented. In full analogy with the recentq=1 conjecture of Singhet al. [1], the corresponding Green's function is constructed in terms of the extended continued fraction. For the simplest example withV(r)=r²+²r⁴, its convergence is proved and the resulting energy spectrum is numerically tested.

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