Consider the Spin Hamiltonian: Ĥ = -Aox where A e R is a non-negative real number. Use as a trial wave function: |(0)) = cos(0/2) |+z) + sin(0/2) |-z) (a.) What is the exact ground state and exact ground state energy for this Hamiltonian? (b.) Using the trial wave function, calculate E(0), the energy as a function of the parameter 0. (c.) Using the variational principle, estimate the ground state energy. How good is your solution and why?

Consider the Spin Hamiltonian: Ĥ = -Aox where A e R is a non-negative real number. Use as a trial wave function: |(0)) = cos(0/2) |+z) + sin(0/2) |-z) (a.) What is the exact ground state and exact ground state energy for this Hamiltonian? (b.) Using the trial wave function, calculate E(0), the energy as a function of the parameter 0. (c.) Using the variational principle, estimate the ground state energy. How good is your solution and why?