矩阵输入测试

$$\sigma _z  = \left( \begin{array}{*{20}c}    1 & 0  \\    0 & { - 1}  \\ \end{array}  \right)$$

$$\left| {\psi (t)} \right\rangle  = \left( \begin{array}{*{20}c}    \cos\theta  \\    \sin\theta  \\ \end{array} \right)$$

$$\left| {\psi (t)} \right\rangle  = \left( \begin{array}{*{20}c}    {\cos \frac{\theta }{2}}  \\    {\sin \frac{\theta }{2}}  \\ \end{array}  \right)$$
 

$$\left| {\psi (t)} \right\rangle  = \left( \begin{array}{*{20}c}    {\cos \frac{\theta }{2}}  \\   {\sin \frac{\theta }{2}}  \end{array}  \right)$$

$$\left| {\psi (t)} \right\rangle  = \exp (\mu Bt\sigma _z \frac{i} {\hbar })$$
$$= \left( \begin{array}{*{20}c}    \exp (\mu Bt\frac{i}{\hbar })\cos \frac{\theta }{2}  \\    \exp (\mu Bt\frac{i}{\hbar })\sin \frac{\theta }{2}  \end{array} \right)$$

$$\left| {\psi (t)} \right\rangle  = \left( {\begin{array}{*{20}c}    {\cos \frac{1}{2}} & {\sin \frac{1}{2}}  \\    {\sin \frac{1}{2}} & {\cos \frac{1}{2}}  \\  \end{array} } \right)$$