A quantum mechanical particle in has the initial wave function y = v,r)+ v,(r where and y, are the real wave functions in the ground and first excited state of

A quantum mechanical particle in has the initial wave function y = V,r)+ V,(r where and y, are the real wave functions in the ground and first excited state of the Hamiltonian with energy E, and E respectively . What is expression of probability density at time . (a) b) st)=,(f +|w.f -2/,x)u, ()cos(E,-E) d) lw(x.t) =w, (x) +u, (x)}-2 (x)w (x)cos (E, + E, )