Why is the expectation value of momentum negative? (QM)

[laser1]

Homework Statement

Find <p^2>

Relevant Equations

NA

psi is given above. I have checked multiple times but can't find my mistake. Thank you!

 

[PeroK]

My first thought is that you have to split the integral because of the modulus.

 

[hutchphd]

This is a bound state (can you tell me what fictitious potential?) Does it make sense now?

 

[vela]

If you calculate it as $\langle \psi \rvert p^2 \lvert \psi \rangle = \langle p\psi \vert p\psi \rangle$, you'll get a positive answer. My guess is that it's the discontinuity in $\psi'$ at $x=0$ that's causing your problem.

 

[pines-demon]

Distributionally
$$\frac{\mathrm d^2 }{\mathrm d x^2} (e^{-\lambda |x|})= \lambda^2 e^{-\lambda|x|}-2\lambda \delta(x)$$