BOOK: Quantum Mechanics, A Paradigms Approach, David H. McIntyre

CHAPTER: 7, 8 AND 9.

Please solve the following problems.

51. For a hydrogen atom whose state at: = 0 is given by LF : A (/1300 + % $211 + f (#100 5 3 (a) Determine the expectation value of the energy (b) Determine the expectation value of L2 (c) Determine the expectation value of LC 52. For a hydrogen atom whose state at: = 0 is given by '1' = A 111300 + % $211 + i (#100 (a) Determine the expectation value of the energy (b) Determine the expectation value of L2 (c) Determine the expectation value of Ll 53. Consider two identical particles each with angular momentum 1' = 1. Denoting the angular momentum states of each particle by |F = l, m)] and |f = l, m')2 then eigenstates of L2 = L2\") +L2l2l can be written as |t' = 1, m)1|f = 1, m'); with eigenvalue m2 = m +m'. (a) Construct the eigenstate with the largest value of mZ (What total 1' = (max must this state correspond to?) (b) Using the total lowering operator L- = L-(I) +L_[2), determine all the states with successively smaller values of mz. (c) Construct a new eigenstate by using orthogonality on the state of {max with m2 = fmax 1. (What total F must this state correspond to?) (d) Generate all lower mz states using the total lowering operator. (e) Continue this procedure until all states of [L2 and L2. (Follow the procedure used in class to nd the states of j = g and j = 1 from the l' = l and s = % states. 2