Please answer this as soon as you can. Thank you so much!

Question 1 (20 points) We start with a. system in the following state which is a super position of harmonic oscillator states |7;v) : C' [(1 + 7')|0) + 3|1) + |2)] Where the oscillation frequency is we a) Find the normalization constant C (3 points). 1)) Find the expectation value for the ladder operator ((1) (3 points) 0) Find the expectation value for the ladder operator (al) (3 Points). d) Find the expectation value (H) where H is the harmonic oacillator Hamiltonian (3 points)? 0) Find the time evolution for the state |7;v(t))? (3 points)