Re: Strongly coupled quantum mechanics

From: David (soroastro2001_at_yahoo.co.uk)
Date: 06/28/04 

Date: 28 Jun 2004 13:10:37 -0400

Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote in message news:<cba9bj$u0r$1@lfa222122.richmond.edu>...

> David wrote:

> > Can anyone suggest what can be said about (say) 0+1 dimensional
> > quantum mechanics in the limit where kinetic terms are suppressed?

> This is just the infinite mass limit of a system. The system becomes
> very slow and behaves essentially classically, if started in a coherent
> state.

I think I have become confused, because carrying out this process
would naively seem to result in a non-propagating theory in which the
wavefunction converges to \delta(x_0) for all time, for a particle
which has initial conditions x=x_0 at t=t_0. But, this isn't what I
would like to understand as a classical limit, in which I would prefer
kinetic terms to be still present. Have I misunderstood?

Despite my confusion, then, am I correct in supposing that the
amplitude for a particle to propagate from x_a to x_b, in a quantum
theory without kinetic terms, is just \delta(x_a - x_b), appropriately
normalized by the volume of space?