Using S, and St as needed, answer the following: (a) Calculate and write out the matrix representing the time evolution operator (t) in the {lam)} representation (see problem 1(h)]. Take time to do this carefully, and simplify matrix elements as much as possible; they should all reduce to simple sine and cosine functions (p.123 of the QM Field Guide might help). Note that this is the longest single calculation of the exam. (b) Calculate and write out the matrix representing in the {un)} representation. Be careful here! Note how S was defined, and note the representation you are coming from and transforming into! (As one check on your final answer, consider whether this matrix should be Hermitian, uni- tary, both, or neither, and see if you result is consistent with what you expect.) (c) Check your work for part 4(b) by calculating the eigenvalues of the matrix that you wrote out. Are they what they should be? If you think you have made an error, specify what the eigen- values should be. Using S, and St as needed, answer the following: (a) Calculate and write out the matrix representing the time evolution operator (t) in the {lam)} representation (see problem 1(h)]. Take time to do this carefully, and simplify matrix elements as much as possible; they should all reduce to simple sine and cosine functions (p.123 of the QM Field Guide might help). Note that this is the longest single calculation of the exam. (b) Calculate and write out the matrix representing in the {un)} representation. Be careful here! Note how S was defined, and note the representation you are coming from and transforming into! (As one check on your final answer, consider whether this matrix should be Hermitian, uni- tary, both, or neither, and see if you result is consistent with what you expect.) (c) Check your work for part 4(b) by calculating the eigenvalues of the matrix that you wrote out. Are they what they should be? If you think you have made an error, specify what the eigen- values should be