New Quantization Method for Evaluation of Eigenenergies

A quantum dynamical equation is constructed as the limit of a sequence of functions (called Semiquantum momentum functions or SQMF). The quantum action variable J is defined as the limit of the sequence of contour integrals of SQMFs such that the quantization condition is J = n, where n is a nonnegative integer for eigenvalues and a noninteger for off eigenvalues. This quantization condition is exact and J is an analytic function of energy. Based on new definitions, an accurate numerical method is developed for obtaining eigenenergies. The method can be applied to both real and PT symmetric complex potentials. The validity and the accuracy of this new method is demonstrated with three illustrations.     

Hypervirial perturbation theory for eigenenergies for two types of atomic potentials

Eigenenergies are calculated for the potentialsV ₁(r)=−(a/r)[1+(1+br)e^−2br ] andV ₂(r)=−(v/r)[1 −λr(1−Z ⁻¹)(1+λr)⁻¹], using renormalized series technique. Accurate results produced here for various eigenstates agree with those available in the literature.     

形如Coulomb势的本征值微扰计算

用超位力定理(HVT)和赫尔曼-费恩曼(Hellman-Feynman)定理(HFT)计算了Coulomb势加上径向线性项和常数项的本征能量的微扰系数,这种计算方法优于通常的瑞利-薛定谔微扰理论,不需要计算本征函数系数,并且用这种方法可以既快捷又有效地计算大量本征能量的微扰系数.