论文部分内容阅读
应用超球坐标表示氦原子和氢负离子的薛定谔方程。将二电子原子在三维空间中的运动转化为单电子原子在六维空间中受广义库仑力作用的运动。我们给出了六维空间广义角动量算符的本征值与本征函数,并以此本征函数做基构造超球波函数,得到超球径微分方程。以广义Laguerre多项式表示超球径波函数,运用密度矩阵和线性变分法得到非正交基下超球径波函数满足的久期方程,最后求得能量和波函数。计算结果与精确的计算符合良好。
The Schrödinger equation for the helium atom and the hydride ion is represented by the hypersphere coordinates. The movement of two-electron atom in three-dimensional space is transformed into the movement of single-electron atom by Coulomb force in six-dimensional space. We present the eigenvalues and eigenfunctions of the generalized angular momentum operator in the six-dimensional space, and use this eigenfunction to construct the hypersphere wave function and obtain the hypersphere diameter differential equation. The generalized Laguerre polynomial is used to represent the hypersphere diameter wave function. The density matrix and linear variation method are used to get the secular equation which satisfies the non-orthogonal base-sphere diameter wave function. Finally, the energy and wave function are obtained. The calculation results are in good agreement with the exact calculation.