动量对于时间的导数等于势能对于距离的导数

自己最近在努力学习量子力学,看到Ehrenfest’s theorem: the expected values in Quantum Mechanics obeys the classical laws. 现在证明动量对于时间的导数等于势能对于距离的导数,即: (1)   First by definition, we have: (2)   (3)   How do we proof the equality? First we notice that the norm of the wave function can be expressed the following: (4)   so (3) can be expanded as:     …