径向情况下原点附近波函数的行为

关于Schroedinger径向方程原点处Dirac δ项的出现

On the appearance of a Dirac delta term at the origin in the Schroedinger radial equation

本文回顾了最近关于中心势薛定谔径向方程原点边界条件的讨论。使用通常的球坐标的一个轻微的修改，以前报道的狄拉克δ函数项在原点的原点清楚地显示了。因此，在求解径向方程时，无论势的种类如何，都必须在原点处施加一个消失的边界条件。

粒子直接相互作用是量子行为的起源

Direct particle interaction as the origin of the quantal behaviours

有人认为，量子行为可以理解的直接粒子相互作用的框架。介绍了一个具体的例子。假设的势预测，在足够大的距离量子行为的出现，而在非常大的距离引力类力的存在。如果所有粒子都有内部结构，则后者是正确的。

Comments about the boundary condition for reduced radial wave function in multi-dimensional equation

The problem of boundary behaviour at the origin of coordinates is discussed for D-dimensional Schrodinger equation in the framework of hyper spherical formalism, which have been often considered last time. We show that the Dirichlet condition, which seems as natural, is not mathematically well justified, on the contrary to the 3-dimensional case. The stronger argument in favour of Dirichlet boundary condition is the requirement of time independence of wave functions norm. The problem remains open for singular potentials.

尊重其渐近行为的连续态波函数的复高斯表示

A complex Gaussian representation of continuum wavefunctions respectful of their asymptotic behaviour

本文优化复高斯基组以准确表示连续态径向波函数，提出一种间接拟合方法，在保持渐近振荡行为的同时将高斯表示应用于有限空间的畸变因子，并保留了分子电离应用中单电子跃迁积分的解析结构。

Singular Behavior of the Laplace Operator in Polar Spherical Coordinates and Some of Its Consequences for the Radial Wave Function at the Origin of Coordinates

Singular behavior of the Laplace operator in spherical coordinates is investigated. It is shown that in course of transition to the reduced radial wave function in the Schrodinger equation there appears additional term consisting the Dirac delta function, which was unnoted during the full history of physics and mathematics. The possibility of avoiding this contribution from the reduced radial equation is discussed. It is demonstrated that for this aim the necessary and sufficient condition is requirement the fast enough falling of the wave function at the origin. The result does not depend on …

薛定谔方程径向波函数的边界条件是什么？

What is the boundary condition for radial wave function of the Schrödinger equation ?

在数学物理文献和量子力学教科书中有很多关于球对称势的讨论。然而，关于径向函数在原点的行为，特别是对于奇异势，还没有达成共识。仔细推导径向薛定谔方程，当拉普拉斯算子写在球坐标中时，会出现δ函数项。结果，不管势的行为如何，在径向波函数上以在原点处消失的边界条件的形式施加了附加约束。