I am self-studying from a text in QM. Well defined states are mentioned several times. By and large these are consistent and seem to be readily apparent:

states of well defined energy are basis kets

if $Q$ is an observable, any arbitrary ket can be represented as a linear combination of states {$q_i$} in which values of $Q$ are well defined

whenever $[Q,H] = 0$, a state of well defined $Q$ evolves into another such state.

So far so good. Then comes the "bombshell."

The text later on says:

States of w-d energy are **unphysical** and
**never occur in Nature**. They are incapable of
changing in any way, and hence it is impossible
to get a system into such a state.

I would appreciate any explanations reconciling these two apparently contradictory characterizations of well defined states. And, in particular, how then to understand, e.g., a creation operator in the case of a harmonic oscillator in a stationary state.

**EDIT** Hopefully there might be any answer regarding the last part of the question regarding harmonic oscillators. From the perspective of a naive beginner, it looks like the analysis is a representation of reality.

As I think about this, one thing that comes to mind is that the creation and annihilation operators are not Hermetian, with my presumed inference that this undermines the "reality" of the model.

But in view of the highlighted quote, it seems that it is but an exquisite mathematical exercise. To the extent this is accurate, then what is the relevance of studying it. I would hazard a guess that it might be a framework for studying the anharmonic oscillator.

This post imported from StackExchange Physics at 2014-04-24 02:30 (UCT), posted by SE-user Andrew