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Exact Solutions of the Schrodinger Equation with a Spherical Harmonic Oscillatory Ring Shaped Potential
Pages: 63-67
Year: Issue:  5
Journal: Journal of Chongqing Normal University(Natural Sci

Keyword:  非中心势 薛定谔方程 Nikiforov-Uvarov方法 束缚态;
Abstract: 本文在新的环状非球谐振子势的基础上研究了一种新的非中心势,称之为球谐环状震荡势V(r,θ)=1/2Mr2ω2+2/2Mr2(η+A cos2θ+B cos4θ/sin2θcos2θ)。用Nikiforov-Uvarov方法进行了研究,求出了球谐环形振荡势条件下的薛定谔方程的精确解Km()=1/2π~(1/2)exp(im)。其角向和径向方程的束缚态的解可以用罗德里格斯公式、广义超球多项式和广义拉盖尔多项式来表示,分别为Hn=C’nx(1-x)-b/2F-(n,n+a/2+b+1,a/2+1)x,ynr(s)=Lμnr(s),Bnr=1/(2nrn!),μ=1/2(1+4Λ)~(1/2)。
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