3-D Schrodinger Equation

三维薛定谔方程

In three dimensions, the time-independent Schrodinger equation takes the form

在三维情况下，时间无关的薛定谔方程形式为

for cartesian coordinates. This can be written in a more compact form by making use of the Laplacian operator

对于笛卡尔坐标系而言，这可以借助拉普拉斯算子写成更紧凑的形式。

The Schrodinger equation can then be written:

薛定谔方程可以写成：

For systems with a spherically symmetric potential, like the hydrogen atom, it is advantageous to use spherical coordinates.

对于具有球对称势的系统，如氢原子，使用球坐标是更有利的。

Index

Schrodinger equation concepts

索引：薛定谔方程概念

HyperPhysics***** Quantum Physics

HyperPhysics ***** 量子物理

Go Back

Schrodinger Equation, Spherical Coordinates

薛定谔方程，球坐标

If the potential of the physical system to be examined is spherically symmetric, then the Schrodinger equation in spherical polar coordinates can be used to advantage. For a three-dimensional problem, the Laplacian in spherical polar coordinates is used to express the Schrodinger equation in the condensed form

Expanded, it takes the form

This is the form best suited for the study of the hydrogen atom.

如果所研究的物理系统的势是球对称的，那么在球坐标中使用薛定谔方程会很有优势。对于三维问题，使用球坐标中的拉普拉斯算符来表达薛定谔方程的简化形式。展开后形式为：这是研究氢原子的最佳形式。

Index

Schrodinger equation concepts

索引：薛定谔方程概念

HyperPhysics***** Quantum Physics

HyperPhysics ***** 量子物理

Go Back