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Re: Quantum question?



Chuck Britton wrote:

While the Heisenberg's Uncertainty relation may not EXPLICITLY 'come
from' the Schrodinger equation, I was told that ANY wave formulation
contains this limit IMPLICITLY.

I am not mathematically sophisticated enough to decipher Schrodinger's
equations
myself, but Chuck's statement represents the understanding I brought to the
original question. I thought that the results of Schrodinger's equations were
inherently "fuzzy" because of the Uncertainty Principle. Is this not correct?

I'm not an expert, but I will try to phrase my conceptual
grasp of this question.

The eigenfunctions which are solutions to Schrodinger's time
independent equation represent stable and metastable states*
of a system. Nothing is said about their longevities. In
order to calculate those the radiation field** must be coupled
to the system, as Jack pointed out. Solving the time dependent
Schrodinger equation with the expanded Hamiltonian should, in
principle, yield descriptions of atoms undergoing transitions,
but of course those solutions are inaccessible to calculation,
and perturbative approximations are used instead. The results
are indeterminate to the degree imposed by Heisenberg's
indeterminacy principle; I guess one could say that the
details of the time evolution of atomic systems is "fuzzy".
The fuzziness derives, I believe, from the indeterminacy of
the phase of the time dependent part of the wave function.
Schrodinger's equation does not yield this phase; it is
indeterminate.

(My explanation may also be fuzzy!)

Leigh

* stationary states

** or any other relevant relatively weak interaction terms,
such as those due to neighboring atoms