A particle is moving in one dimension subject to some potential function U. At the instant t = 0, the wave function of the system happens to be completely real. Show that the wave function at all...

A particle is moving in one dimension subject to some potential function U. At the instant t = 0, the wave function of the system happens to be completely real. Show that the wave function at all times satisfies

Comment on the following: If the wave function is ever real, the future of the system is a perfect reflection of its past.