Recent content by PatsyTy

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    Optics Lab Project Holographic Weapon Sight

    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...
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    Optics Lab Project Holographic Weapon Sight

    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...
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    Density Operator to Matrix Form

    Thank you, that makes sense!
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    Density Operator to Matrix Form

    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.
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    Density Operator to Matrix Form

    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|##...
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    Time-Dependent Perturbation Theory

    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)|...
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    Time-Dependent Perturbation Theory

    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!
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    Time-Dependent Perturbation Theory

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

    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...
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    Normalization of the Angular Momentum Ladder Operator

    Thanks! I got it right away with that.
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    Normalization of the Angular Momentum Ladder Operator

    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##...
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    Momentum and Position Operator Commutator Levi Civita Form

    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...
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    Particular Solution of A Coupled and Driven Oscillator

    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...
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    Particular Solution of A Coupled and Driven Oscillator

    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: $$...
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    Real Part of Gain of LRC Circuit

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