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## 角动量和磁矩

(2019-01-21 21:48:03)

## 1.电子的磁矩

### 玻尔磁子

https://math.jianshu.com/math?formula=g_L%20=%201

https://math.jianshu.com/math?formula=g_S%20=%202

https://math.jianshu.com/math?formula=L_z%20=%20m%20/hbar,%20m%20=%200,%20/pm%201,%20...%20,%20/pm%20l

### 拉莫频率

Direction of precession for a negatively-charged particle. The large arrow indicates the external magnetic field, the small arrow the spin angular momentum of the particle.

https://math.jianshu.com/math?formula=U%20=%20-%20B%20/cdot%20/mu%20=%20-%20B%20/mu%20/cos%20/theta

i.e.,

https://math.jianshu.com/math?formula=/omega_L是电子做轨道运动时的进动频率, 也叫拉莫频率(Larmor frequency)。

https://math.jianshu.com/math?formula=/omega%20=%20g%20/omega_L

https://math.jianshu.com/math?formula=/omega_S%20=%202%20/omega_L

### 旋磁比

https://math.jianshu.com/math?formula=/vec%20/mu%20=%20/gamma%20/vec%20J

https://math.jianshu.com/math?formula=g_S%20=%202.00231930436153

### 斯特恩-盖拉赫实验

https://math.jianshu.com/math?formula=3%20k_B%20T%20=%200.155%20eV

https://math.jianshu.com/math?formula=/mu_z%20=%20-2%20/mu_B%20m_S

https://math.jianshu.com/math?formula=/mu_z%20=%20/mp%20/mu_B

https://math.jianshu.com/math?formula=/Delta%20=%20/tan%20/theta%20/times%201%20=%200.037%20m

https://math.jianshu.com/math?formula=2%20/Delta%20=%200.074%20m

## 2.角动量相加和朗德因子

https://math.jianshu.com/math?formula=J%20=%20L%20+%20S

### 角动量相加

https://math.jianshu.com/math?formula=J, https://math.jianshu.com/math?formula=L, https://math.jianshu.com/math?formula=S三个向量一起构成一个三角形, 根据三角形的性质(两边之和大于第三边, 两边只差小于第三边), 应满足:

https://math.jianshu.com/math?formula=/left

https://math.jianshu.com/math?formula=J_z%20/left

https://math.jianshu.com/math?formula=j%20=%20l+s,%20l+s-1,%20...%20,%20/left

https://math.jianshu.com/math?formula=j%20=%201-1/2%20=%201/2

### 总磁矩

https://math.jianshu.com/math?formula=/mu_J%20=%20/mu_S%20/cos%20(S,%20J)%20+%20/mu_L%20/cos%20(L,%20J)

### 在磁场中的能量

https://math.jianshu.com/math?formula=U%20=%20-%20/mu_J%20/cdot%20B

https://math.jianshu.com/math?formula=U%20=%20g_J%20m_J%20/mu_B%20B

https://math.jianshu.com/math?formula=m_J%20=%20J,%20J-1,%20...,%20-J

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