A particle in a harmonic oscillator potential has the Hamiltonian: Ĥ₁ = p² + 1 mo²x² Define the raising the raising and lowering operators: a â √2h 1 √2hmw 1 2hmw 2m 2 -(-ip+mox) and =(ip+mwx). Then ⸥₁ = √n+¹⁄+_and_ây = √mp-1, where y denotes the normalized eigenfunction of Ĥ with eigenvalue (n + 1) hw. (a) Find the position uncertainty σ, and the momentum uncertainty σ when the harmonic oscillator is in the state 4. (10 marks) (b) Derive the commutation relation [ââ‚â]. You need to express your answer in terms of â or â, and intermediate step is required. (10 marks)