P = \left< \Psi(x,0) | \Psi(x,0) \right> = \left< \Psi(x,t) | \Psi(x,t) \right> = \left< \Psi(x,0) \left| \mathscr{U}^{\dagger} \mathscr{U} \right| \Psi(x,0) \right>