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

  • Thread starter Thread starter laser1
  • Start date Start date
AI Thread Summary
The discussion centers on the negative expectation value of momentum in quantum mechanics, with participants examining the implications of the wave function psi. There is an emphasis on the need to split the integral due to the modulus, and the concept of a fictitious potential is raised. The calculation of momentum squared is highlighted, suggesting it yields a positive result. A key point is the discontinuity in the derivative of psi at x=0, which may be contributing to the observed issue. The conversation underscores the importance of understanding distributional derivatives in this context.
laser1
Messages
166
Reaction score
23
Homework Statement
Find <p^2>
Relevant Equations
NA
1743263023481.png


psi is given above. I have checked multiple times but can't find my mistake. Thank you!
 
Physics news on Phys.org
My first thought is that you have to split the integral because of the modulus.
 
This is a bound state (can you tell me what fictitious potential?) Does it make sense now?
 
  • Like
Likes renormalize
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.
 
Distributionally
$$\frac{\mathrm d^2 }{\mathrm d x^2} (e^{-\lambda |x|})= \lambda^2 e^{-\lambda|x|}-2\lambda \delta(x)$$
 
  • Like
Likes vela, laser1, TSny and 2 others
Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'
(Disclaimer: this is not a HW question. I am self-studying, and this felt like the type of question I've seen in this forum. If there is somewhere better for me to share this doubt, please let me know and I'll transfer it right away.) I am currently reviewing Chapter 7 of Introduction to QM by Griffiths. I have been stuck for an hour or so trying to understand the last paragraph of this proof (pls check the attached file). It claims that we can express Ψ_{γ}(0) as a linear combination of...
Back
Top