An unchanging quantum universe

This another one of those bizarre thoughts that cosmology throws up which manages to be both simple and profound.

Imagine the wave function for the whole universe.

By its nature the universe cannot change its quantum state: it’s the ultimate closed system. Of course there is a  probabilistic distribution of energy inside the system but the total energy of the system does not change and therefore its quantum state cannot change either.

So, in quantum terms the universe is unchanging over time.