How Do You Calculate the Expectation Value of Momentum in Quantum Mechanics?

[atomicpedals]

I've managed to get myself confused on a seemingly simple point of mathematics. When I calculate the expectation value of momentum in quantum mechanics

$$<p>=\int{\psi* \frac{\hbar}{i} \frac{d}{dx} \psi dx}$$
To what should I be applying the derivative? $\psi$?

 

[Dick]

Of course you would apply it to ψ. What else?

 

[atomicpedals]

Order of operation would rule out complex conjugate of $\psi$. So, instead of being like <x> which can simplify to

$$<x>=\int{|\psi|^{2}xdx}$$
it would instead be
$$<p_x>=\int{\psi * \frac{\hbar}{i} \frac{d \psi}{dx} dx}$$

 

[Dick]

Order of operation would rule out complex conjugate of $\psi$. So, instead of being like <x> which can simplify to

$$<x>=\int{|\psi|^{2}xdx}$$
it would instead be
$$<p_x>=\int{\psi * \frac{\hbar}{i} \frac{d \psi}{dx} dx}$$

Yes. That's it.

 

[atomicpedals]

Right on, thanks.