Complex sentence: This intuitive picture is not quite right, because\\ psi ^ is an eigenfunction of the Hamiltonian and so at different times only differs by a phase, and so in particular the physical state does not evolve and so it cannot become noninteracting.
Split into simpler sentences: This intuitive picture is not quite right, because\\ psi ^ is an eigenfunction of the Hamiltonian and so at different times only differs by a phase. Thus, in particular, the physical state does not evolve and so it cannot become noninteracting.