3. Fine structure and Zeeman on equal footing In class we saw that in the intermediate regime the Zeeman effect and the fine structure splitting should be considered as one perturbation. This regime is the most complicated but its results should hold even in the other regimes (why?). It is therefore worth while to know how to calculate the correction this way. (a) Write a computer program to calculate the matrix elements of Wiy for the subspace of degenerate eigen states 1m;m,, Note that we're using a different basis from the book. Your program should be able to build a 2n2 x 2n2 matrix for any n. Use the known expectation values for 1/r, 1/r2 and 1/r3 in terms ofl (b) Prepare the matrix for n = 2 and for n = 3 and numerically diagonalize it for some field strength B. Plot the corrections to the energy as a function of B. (c) Focus on the n 2 case. Plot the energies in the high field and low field limits (which we have derived in class) as a function of the field B and plot these graphs together with the numerical solution you found above. Comment about the regimes of validity. 3. Fine structure and Zeeman on equal footing In class we saw that in the intermediate regime the Zeeman effect and the fine structure splitting should be considered as one perturbation. This regime is the most complicated but its results should hold even in the other regimes (why?). It is therefore worth while to know how to calculate the correction this way. (a) Write a computer program to calculate the matrix elements of Wiy for the subspace of degenerate eigen states 1m;m,, Note that we're using a different basis from the book. Your program should be able to build a 2n2 x 2n2 matrix for any n. Use the known expectation values for 1/r, 1/r2 and 1/r3 in terms ofl (b) Prepare the matrix for n = 2 and for n = 3 and numerically diagonalize it for some field strength B. Plot the corrections to the energy as a function of B. (c) Focus on the n 2 case. Plot the energies in the high field and low field limits (which we have derived in class) as a function of the field B and plot these graphs together with the numerical solution you found above. Comment about the regimes of validity