一个新的精确可解的三维解析势

A New Exactly Soluble 3-dimensional Analytical Potential

提出了一种新的精确可解的三维解析势函数 ,即环形非球谐振子。势函数为 V(r,θ) =12 mω2 r2 + 22mAr2+ 22mbr2 sin2 θ.将环形非球谐振子势的Schr dinger方程在球坐标系中进行变量分离 ,得到了角向方程和径向方程 ,给出了精确的能谱方程 ,获得了用普遍的associated -Legendre多项式表示的归一化的角向波函数和用合流超几何函数表示的归一化的径向波函数。球谐振子、非球谐振子和环形振子的有关结果均作为特例包含在本文的一般结论之中。

A new exactly soluble 3-dimensional analystical potential, i. e. ring shaped nonspherical oscillator (RSNSO), is proposed in this paper as V(r,θ)=12mω 2r 2+ 22m Ar 2+ 22m br 2 sin 2θ. The Schrdinger equation with a ring shaped non-spherical oscillator (RSNSO) potential is solved by using the usual method of variable separation. The exact energy equation is obtained. The normalized angle wavefunctions expressed in terms of the universal associated-Legendre polynomials and the normalized radial wavefunctions expressed in terms of the confluent hypergeometric function are presented. The relevant results of ring shaped oscillator (RSO), Non-Spherical Oscillator (NSO), and Spherical Oscillator (SO) reported in the references are contained in conclusions of this paper as special cases.