i) Consider the harmonic oscillator raising and lowering operators: mw . . at V2 Vmhw 1 mw . . a = V2 ac + Px Vmhw Show that they obey the commutation relation a, at] = 1. Hint: you will need the commutation relation [x, Px] = ih. [4 marks] ii) Show that the harmonic oscillator Hamiltonian: H = =mw 2 82 + 1 2 2m Px can be written as: H = hwata+ ? 2