Given in problem
The Attempt at a Solution
a) I've been able to find expressions of operators x, p_x, y and p_y in terms of the creation/annihilation operators and hence been able to express the angular momentum operator as:
However, I'm having trouble just writing the operators x, p_x, y and p_y in terms of the "new" creation/annihilation operators and so I can proceed to find J_z in terms of the new operators.
b) I'm guessing I need to formulate an eigenequation involving J_z and H to find the eigenstates of J_z? I'm pretty stumped on this question to be honest.