Re: Why isn't the constant force problem covered in Quantum Mechanics?

t_pellman@xxxxxxxxxxx wrote:
> Why isn't the constant force problem covered in Quantum Mechanics
> texts? I checked a dozen and found no reference, even in the very
> thorough Messiah text. I can find very little on the web. One would
> think that it would be first thing covered after the free particle.

Do you mean the situation where there is a potential that
does not depend on time? That is, V(x) not V(x,t)? That
is certainly covered in many texts for a variety of V's.

Or do you mean the case where V(x) = K x, that is, a particle
in a constant slope potential? I can't recall that one ever
being done. It may be that people consider it unphysical
because it's hard to figure out your boundary conditions.
Think of what you would have to put in for the very distant
past or the far future. Things blow up.

I've seen people do things like turn on a potential such
as that at t=0, then turn it off again at t=T, and work
out the result.

I have seen various steps and ramps between plateaus done
in various texts or courses. In general, this becomes fairly
tedious to do in closed form and starts to call for a numeric
solution. Did that in at least one undergrad quantum course.
A ramp like that between two plateaus might be made to look
somewhat like an accelerator.
Socks

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