Magnetic Interactions and the
Lande' g-Factor

磁相互作用与兰德 g 因子

A magnetic moment experiences a torque in a magnetic field B. The energy of the interaction can be expressed as

Both the orbital and spin angular momenta contribute to the magnetic moment of an atomic electron.

轨道角动量和自旋角动量都对原子电子的磁矩有贡献。

.
where g is the spin g-factor and has a value of about 2, implying that the spin angular momentum is twice as effective in producing a magnetic moment.

磁矩在磁场B中会受到力矩的作用。相互作用的能量可以表示为。其中g是自旋g因子，其值约为2，这意味着自旋角动量在产生磁矩方面是两倍有效的。

The interaction energy of an atomic electron can then be written

原子电子的相互作用能可以写成

which when evaluated in terms of the relevant quantum numbers takes the form

当用相关的量子数来表示时，其形式为

Show evaluation process

展示评估过程

Zeeman interaction

塞曼相互作用

Anomalous Zeeman effect

异常塞曼效应

Index

Schrodinger equation concepts

Hydrogen concepts

索引希尔伯特方程概念氢原子概念

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Evaluating the Lande' g-Factor

计算兰德 g 因子

The Lande' g-factor is a geometric factor which arises in the evaluation of the magnetic interaction which gives the Zeeman effect. The magnetic interaction energy

which is continuous in the classical case takes on the quantum form

在经典情况下连续的，在量子情况下则呈现为量子形式

which is like a vector operation based on the vector model of angular momentum

这类似于基于角动量矢量模型的矢量运算

兰德-g因子是一个几何因子，出现在计算磁相互作用以解释塞曼效应的过程中。磁相互作用的能量

The problem with evaluating this scalar product is that L and S continually change in direction as shown in the vector model. The strategy for dealing with this problem is to use the direction of the total angular momentum J as a coordinate axis and obtain the projection of each of the vectors in that direction. This is done by taking the scalar product of each vector with a unit vector in the J direction.

These vector relationships must be evaluated and expressed in terms of quantum numbers in order to evaluate the energy shifts. Carrying out the scalar products above leads to

这些矢量关系必须被评估并用量子数表示，以便计算能量变化。进行上述标量积运算将得到