# 可分離變數的偏微分方程

${\displaystyle F=F_{1}(x_{1})F_{2}(x_{2})\cdots F_{n}(x_{n})}$

## 範例

${\displaystyle [-\nabla ^{2}+V(\mathbf {x} )]\psi (\mathbf {x} )=E\psi (\mathbf {x} )}$

${\displaystyle V(x_{1},x_{2},x_{3})=V_{1}(x_{1})+V_{2}(x_{2})+V_{3}(x_{3}),}$

## 參考資料

1. ^ L. P. Eisenhart, "Enumeration of potentials for which one-particle Schrodinger equations are separable," Phys. Rev. 74, 87-89 (1948).