Two non-interacting identical spin 3/2 particles are confined in a three-dimensional harmonic oscillator. (a) (5 points)...

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Two non-interacting identical spin 3/2 particles are confined in a three-dimensional harmonic oscillator. (a) (5 points) Find the energy of the ground state, and the corresponding eigenvectors. Express your answers in terms of the total spin. Hint: be careful that the overall symmetry of the wave function is satisfied. Now suppose that a small perturbation of the form, H' = λ S₁ S₂ is added. Where S₁ and S₂ are respectively the spin operators of the first and second particle, and A> 0 a small positive parameter. (b) (5 points) Evaluate the first order correction(s) to the energy of the ground state and represent your results on a graph of the energy versus the perturbation. Hint: express the scalar product S₁ S₂ in terms of the total spin vector Two non-interacting identical spin 3/2 particles are confined in a three-dimensional harmonic oscillator. (a) (5 points) Find the energy of the ground state, and the corresponding eigenvectors. Express your answers in terms of the total spin. Hint: be careful that the overall symmetry of the wave function is satisfied. Now suppose that a small perturbation of the form, H' = λ S₁ S₂ is added. Where S₁ and S₂ are respectively the spin operators of the first and second particle, and A> 0 a small positive parameter. (b) (5 points) Evaluate the first order correction(s) to the energy of the ground state and represent your results on a graph of the energy versus the perturbation. Hint: express the scalar product S₁ S₂ in terms of the total spin vector