The purpose of this question is to motivate the introduction of the â and â' operators for the harmonic oscillator system. we will adapt the simple formula (а — іb)(а + ib) = a2+82 for real numbers a and b. (a) take the harmonic oscillator hamiltonian 1 +mu22 — н 2m 2 and write it in the form hw(q22) q and q is proportional to p, and § is proportional to â. find where in terms of p and â. (b) what is the point of factoring out hw? (c) show that [ë, qi = (d) expand (iq)(e + iq) and simplify. (e) hence show that h can be rewritten as q. and relate â and â* to £ and (f) show that [â, â*] = 1. (g) let {|n)} be the orthonormal energy eigenstates of the harmonic oscillation. recall that the energy eigenvalues are hw (n + 2). use the raising and lowering operator formalism to compute (n| f4 |n).