5. Let us consider a particle of mass m in a one-dimensional potential U(x) satisfying the conditions U(x) - 0 as x - 1 co and Uo U(x)dx > 0. (1) Show that in such a potential there exists at least one state of discrete spectrum with negative energy. This can be done by evaluating the average energy of the particle _(x) in a state with the wave function w( x ) =ve "ll. 0 (2) and demonstrating that by appropriate choice of the parameter * one can always make the average energy negative, ie. E(x)