本征效率

A . A．紫外吸收 B . B．OH-离子吸收 C . C．过渡金属离子吸收 D . D．原子缺陷吸收

粒子处于一个一维盒子中,盒子长度为L,若粒子处于能量本征值为<img src='https://img2.soutiyun.com/ask/2020-05-14/958318217859229.png' />的本征态中,求粒子对盒子的壁的作用力有多大.

试以基态氢原子为例证明:ψ不是<img src='https://img2.soutiyun.com/ask/2021-03-17/984828116153074.png' />的本征函数，而是<img src='https://img2.soutiyun.com/ask/2021-03-17/984828125835624.png' />的本征函数。

<img src='https://img2.soutiyun.com/ask/2021-01-25/98043190637097.png' />和<img src='https://img2.soutiyun.com/ask/2021-01-25/980431914693446.png' />对算符<img src='https://img2.soutiyun.com/ask/2021-01-25/980431926750136.png' />是否为本征函数？若是，求出其本征值。

证明<img src='https://img2.soutiyun.com/ask/2020-12-30/978204552292445.png' />是线性谐振子的本征波函数，并求此本征态对应的本征能量，式中A为归一化常数，<img src='https://img2.soutiyun.com/ask/2020-12-30/978204564985171.png' />

下列函数哪些是算符<img src='https://img2.soutiyun.com/ask/2021-03-17/984828718116624.png' />的本征函数，其本征值是什么？ <img src='https://img2.soutiyun.com/ask/2021-03-17/984828735067581.png' />

<img src='https://img2.soutiyun.com/ask/2020-12-30/978207392623903.png' />表示沿z方向平移距离口的算符，证明下列形式波函数(Bloch波函数)： <img src='https://img2.soutiyun.com/ask/2020-12-30/978207402291456.png' /> 是Dx (a)的本征念，相应本征值为<img src='https://img2.soutiyun.com/ask/2020-12-30/978207411124961.png' />