Re: Can we get any quantum state from some classical state by unitary transformation?

whopkins_at_csd.uwm.edu
Date: 01/12/05 

Date: Wed, 12 Jan 2005 19:59:22 +0000 (UTC)

The quantum and classical state spaces are in different superselection
sectors (with the latter corresponding to the value of h = 0 for
Planck's constant). There is no transition between any two states in
any of these spaces nor into or out of any of the state spaces
corresponding to other values of h.

Thus, the Heisenberg algebra
[q^a,q^b] = 0 = [p_a,p_b]; [q^a,p_b] = i h-bar
[q^a,h-bar] = 0 = [p_a,h-bar]
actually gives you entirely different sectors for each value of h-bar,
the classical one being where h-bar = 0.