Geometry of Hydrogen Atom Solution

氢原子解的几何学

The hydrogen atom solution to the Schrodinger equation produces three quantum numbers which can be seen to arise naturally from geometrical constraints on the wavefunction.

氢原子的薛定谔方程解产生了三个量子数，这些量子数可以自然地从波函数的几何约束中得出。

Separated into equations in terms of the spherical coordinates

用球坐标形式分离为方程

the wavefunction takes the form

波函数的形式为

which gives three equations. The equation for each of the three variables gives rise to a quantum number and the quantized energy states of the atom can be specified in terms of these quantum numbers.

这给出了三个方程。每个变量的方程都会产生一个量子数，原子的量子化能级就可以用这些量子数来指定。

Index

Hydrogen concepts

索引氢概念

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Quantum Numbers, Hydrogen Atom

量子数，氢原子

In the solution to the Schrodinger equation for the hydrogen atom, three quantum numbers arise from the space geometry of the solution and a fourth arises from electron spin. No two electrons can have an identical set of quantum numbers according to the Pauli exclusion principle , so the quantum numbers set limits on the number of electrons which can occupy a given state and therefore give insight into the building up of the periodic table of the elements.

在求解氢原子的薛定谔方程时，三个量子数来源于解的空间几何特性，而第四个量子数则来源于电子自旋。根据泡利不相容原理，没有两个电子可以具有相同的量子数集合，因此量子数限制了特定状态中可以容纳的电子数目，从而为元素周期表的形成提供了见解。

R(r) Principal quantum number

R(r) 主量子数

P(θ)	Orbital quantum number 轨道量子数
F(φ)	Magnetic quantum number 磁量子数

	Spin quantum number 自旋量子数