Complex conjugate of the expectation value of momentum

jb646
Messages
10
Reaction score
0

Homework Statement


Compute the complex conjugate of <p> using eq 1.35 (<p>=∫ψ*(h/i)∂/∂x ψ dx) and prove that <p> is real (<p>=<p>*)


Homework Equations


equation 1.35 is given above


The Attempt at a Solution


to take the c.c. don't i just add a minus to the i and switch the stars like so:
<p>=∫ψ(-h/i)∂/∂x ψ* dx
i think that is right, but it seems too simple for what i should be doing. as for the second part, could somebody please nudge me in the right direction.

thanks for all your help.
 
Physics news on Phys.org
Well, now comes the tricky part, shifting the derivative under the integral back to the psi. This is done only under the assumption that the wavefunction is normalized to unity.

Can you do it now ?
 
Thread 'Need help understanding this figure on energy levels'
This figure is from "Introduction to Quantum Mechanics" by Griffiths (3rd edition). It is available to download. It is from page 142. I am hoping the usual people on this site will give me a hand understanding what is going on in the figure. After the equation (4.50) it says "It is customary to introduce the principal quantum number, ##n##, which simply orders the allowed energies, starting with 1 for the ground state. (see the figure)" I still don't understand the figure :( Here is...
Thread 'Understanding how to "tack on" the time wiggle factor'
The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
Back
Top