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At 02:19 PM 1/28/00 +0000, Kirkpatrick, James wrote:
... In the case of Schrodinger's equation this is why it isn't
consistent with special relativity.
Might it not still be consistent with special relativity if the phase
velocity and not the derivative of displacement is greater than c?
==== Before answering that, let's consider an analogy ====
Given the relativistic expression
E^2 - p^2 = m^2
it is child's play (well, college freshman's play) to expand it to lowest
order and recover the classical result
KE = p^2 / 2m
This is a nice illustration of the correspondence principle.
OTOH, starting from the classical non-relativistic result, it is *not*
child's play to discover how to generalize it to the relativistic case.
------------
So it is with quantum mechanics. There exist of course correct equations
of motion for relativistic quantum mechanics, and in the low-velocity limit
they reduce to the Schrödinger equation.
OTOH the Schrödinger equation is not relativistically correct, and you
could stare at it for a verrry long time before it told you the correct
relativistic generalization.