Consider a quantum system wtih three states, and a hamiltonian given by 0 3 4 with ε a small parameter and vo and η are constants. we assume η 0. (a) write the eigenvalues e and eigevectors in0)) of the unperturbed hamiltonian (c = 0) for n = 1,2,3. (b) find the three first-order energies, e for n 1,2,3, due to the perturbation e. (c) find the first-order correction to the three eigenstates, in(1), with n = 1,2,3 ( d set vo = 1 (in units of energy) and η = 0.5. plot the three energies ) and the three energies en) for small e, with n = 1,2,3. (e) set vo-1 and η = 0.5. plot the three components of ln(iy for small ε for n = 1. in the plots, you need to decide how far to plot in ε, since ε must be a small parameter.

Could someone . i have tried to solve myself but my calculation is off

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5submission this assignment is worth 20 points total. you are required to submit the following by next lab: 1. (3 points) determine the equation for the output angular velocity ω2 = θ˙ 2 as a function of θ1, ω1 = θ˙ 1 and α. you must show all your work to receive credit. 2. (2 points) use the result of problem#1 to plot ω2 over 0 ≤ θ1 ≤ 360deg with ω1 = 360deg/sec. do this for α = {10,30}deg. show the results on the same plot and properly label the axes, title, legend. for this you can use matlab or ms excel. 3. (3 points) determine the equation for the output angular acceleration ω˙ 2 and create a plot similar to the one in problem#2. 4. (10 points) submit plots of the results (ω2 and ω˙ 2) obtained from creo/mechanism and compare them to results of problem#2 and problem#3. note that you should do these comparisons for the two cases with α = {10,30}deg. 5. (2 points) provide a brief explanation of the results. did they match? what are the implications as misalignment angle increases?