Two identical spin 1/2 fermions move in one space dimension in the infinite quantum well potential v(x) = 0 for 0 lessthanorequalto x lessthanorequalto l and v(x) = infinity otherwise. write: a) the spatial ground state wave function, and the ground state energy, when the two particles are in a spin-triplet state: b) the spatial wave function for the first excited state, and its energy, when the two particles are in a spin-triplet state: c) the spatial wave function for the second excited state, and its energy, when the two particles are in a spin-triplet state: d) the spatial ground state wave function, and the ground state energy, when the two particles are in a spin-singlet state: e) the spatial wave function for the first excited state, and its energy, when the two particles are in a spin-singlet state: f) the spatial wave function for the second excited state, and its energy, when the two particles are in a spin-singlet state:

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?