Recent content by PatsyTy

Apologies, I meant to link this image: https://upload.wikimedia.org/wikipedia/commons/c/c0/Litepath.jpg Thank you for the information! Glad it has been done in other classes. I'll do some research to see if I can combine the HUD portion with the creating of the hologram. For our lab we are not...

Good evening everyone. For my third year optics course we have to do a research lab that includes a lab component for a project. Our prof has suggested we look into something that interests us an design a lab around it. Personally I have always had an interest in military technology and was...

Thank you, that makes sense!

Thank you, that is what I suspected. How do these cross terms arise from the equation $$\rho=\sum_i p_i|\psi_i><\psi_i$$ It seems that these cross terms do not come from this summation as it is over only one index.

Homework Statement Write the density operator $$\rho=\frac{1}{3}|u><u|+\frac{2}{3}|v><v|+\frac{\sqrt{2}}{3}(|u><v|+|v><u|, \quad where <u|v>=0$$ In matrix form Homework Equations $$\rho=\sum_i p_i |\psi><\psi|$$ The Attempt at a Solution [/B] The two first factors ##\frac{1}{3}|u><u|##...

So I believe the solution is to just change the eigenfunctions to their ket representation and multiply through by ##\langle \psi_b^{(0)} |## i \hbar \sum_k \dot{c}_k (t)\langle \psi_b^{(0)} | \psi_k^{(0)} \rangle e^{-\frac{iE_k^{(0)}t}{\hbar}}=\lambda \sum_kc_k(t)\langle \psi_b^{(0)} | H'(t)|...

Thanks for the reply! I managed to figure it out. I was getting confused thinking ##e^{-iE_k^{(0)}t/\hbar}## was also an operator. When I get home I'll write out what I did to make sure it's correct. Thanks again!

Thanks, I see that now. Guess I'll be taking a look at it tomorrow and see if I can think of another way.

Note this isn't actually a homework problem, I am working through my textbook making sure I understand the derivation of certain equations and have become stuck on one part of a derivation. 1. Homework Statement I am working through my text (Quantum Mechanics 2nd Edition by B.H Bransden & C.J...

Thanks! I got it right away with that.

Homework Statement Obtain the matrix representation of the ladder operators ##J_{\pm}##. Homework Equations Remark that ##J_{\pm} | jm \rangle = N_{\pm}| jm \pm 1 \rangle## The Attempt at a Solution [/B] The textbook states ##|N_{\pm}|^2=\langle jm | J_{\pm}^\dagger J_{\pm} | jm \rangle##...

Homework Statement Prove that ##[L_i,x_j]=i\hbar \epsilon_{ijk}x_k \quad (i, j, k = 1, 2, 3)## where ##L_1=L_x##, ##L_2=L_y## and ##L_3=L_z## and ##x_1=x##, ##x_2=y## and ##x_3=z##. Homework Equations There aren't any given except those in the problem, however I assume we use...

Thanks for the reply! That was my bad actually in copying the question, it does specify in the problem that the frequency of the driving for is equal to ##\sqrt{k/m}##. I believe I managed to get the solution after a couple hours of work by adding the two equations and subtracting the two...

Homework Statement Consider two masses m connected to each other and two walls by three springs with spring constant k. The left mass is subject to a driving force ## F_d\cos(2 \omega t) ## and the right to ## 2F_d\cos(2 \omega t) ## Homework Equations Writing out the coupled equations: $$...

Ah now I see, I need that eye for detail! Thanks again!