Question

\[\frac{\text d \langle {p} \rangle}{ \text{d} t} \]

Answer 1

i need some help where the dots are

Answer 2

it may be integration by parts twice

Answer 3

but i need some help choosing what to integrate and what to differentiate

Answer 4

...

Answer 5

\[= \frac{\hbar}{i}\int\limits_{-\infty}^{\infty}\left( -\frac{i\hbar}{2m}\frac{\partial^2 \Psi^*}{\partial x^2}+\frac{i}{\hbar} V\Psi^*\right)\frac{\partial \Psi}{\partial x}+\Psi^* \frac{\partial}{\partial x} \left(\frac{i\hbar}{2m} \frac{\partial^2 \Psi }{\partial x^2} -\frac{i}{\hbar}V\Psi \right)~\text d x\]

Answer 6

\[\int uv'=uv|-\int vu'\]
\[u=\left( -\frac{i\hbar}{2m}\frac{\partial^2 \Psi^*}{\partial x^2}+\frac{i}{\hbar} V\Psi^*\right)\]\[v'=\frac{\partial \Psi}{\partial x}\]\[v= \Psi\]\[u'=\left( -\frac{i\hbar}{2m}\frac{\partial^3 \Psi^*}{\partial x^3}+\frac{i}{\hbar}\frac{\partial}{\partial x}(V\Psi^*)\right)\]