Problem 5 Use the variational method with three different trial functions (2) = Ae-|! Vz() = A(1 + a[x])e-alal, V3(x) = Aeza/o? where a is a variational parameter to estimate the ground state energy...

Problem 5 Use the variational method with three different trial functions (2) = Ae-|! Vz() = A(1 + a[x])e-alal, V3(x) = Aeza/o? where a is a variational parameter to estimate the ground state energy of a particle of mass m moving in a potential given by V(x) = xl, with = constant. Calculate the difference in their energies (A1,2 = E - E, A2,3 = E9 – Es, A1,3 = Ep - ES)