Two non-interacting identical spin 1/2 particle of mass m are confined in a cube of side...

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Two non-interacting identical spin 1/2 particle of mass m are confined in a cube of side length a. (a) (1 point) Find the energy and wave function of the ground state. What is the degeneracy? Now suppose a small interaction of the form, H' = λ 8(x₁ - x₂)8(¥1 — Y₂) 6(²1 — ²₂) + Xŋ S₁ S₂ - is introduced. Where A is a small positive constant, n a positive parameter, S₁ and S₂ are respectively the spin operators of the first particle and second particle. (b) (5 points) Find the first order correction to the energy of the ground state. (c) (7 points) Repeat part (a) and (b) for two identical spin 1 particles. Comment on the degeneracy. Hint 1: Be careful of the overall symmetry of the wave function! Hint 2: 2n [* dar (sin 17) ²ª = a(2n)! (2n!)² Two non-interacting identical spin 1/2 particle of mass m are confined in a cube of side length a. (a) (1 point) Find the energy and wave function of the ground state. What is the degeneracy? Now suppose a small interaction of the form, H' = λ 8(x₁ - x₂)8(¥1 — Y₂) 6(²1 — ²₂) + Xŋ S₁ S₂ - is introduced. Where A is a small positive constant, n a positive parameter, S₁ and S₂ are respectively the spin operators of the first particle and second particle. (b) (5 points) Find the first order correction to the energy of the ground state. (c) (7 points) Repeat part (a) and (b) for two identical spin 1 particles. Comment on the degeneracy. Hint 1: Be careful of the overall symmetry of the wave function! Hint 2: 2n [* dar (sin 17) ²ª = a(2n)! (2n!)²