Question 1 (15 points) In the quantum harmonic oscillator with oscillation frequency w, we are given the following superposition state, () = C [(1 + ()|0) + (1) + (2)].Find the expectation value for the lowering ladder operator (a)e) Find the expectation value of r; hint: you might want to see if you can write the operator i in a different way (3 points).c) Find the expectation value for the raising ladder operator (at) (3 Points)