Re: THE 'RADIUS' OF THE ELECTRON?

In article <Pine.WNT.4.64.0808021412200.1160@xxxxxxxxx>, Timo A. Nieminen
says...

[snip]

Yes. It follows from the orthogonality of solutions to Schrodinger=B4s eq=
uations.

Hmm. I can write down an orthogonal basis set of solutions to=20
Schroedinger's equation. But there's no requirement for any 2 particular=20
solutions to be orthogonal, and in general they won't be.

True. But (at least as I believed at the time) the implication of Schwinger's
comment was that when you actually do the integrations, it all comes out zero,
because the integrals turn out to be integrals of orthogonal functions.

I have to admit: I am a bit rusty on this kind of computation now, so I was
hoping that you would do it;)


When you do the integral that is the position operator, the orthogonality=
forces
the integral to come out zero.

How do we do this? Clearly not the same as finding P(x,t) =3D |psi(x,t)|=
^2.

Why are you so sure of this? The absolute value is an integral, the integ=
ral
comes out to be zero.

Since when is the absolute value an integral?

You almost proved it yourself below. You gave the -density-, to get the
probability itself you need to integrate it, at least, if you are doing the
probability in a non infinitesimal region.

So yes, if you are really computing the probability that it be at a point, you
need just the density. But then how do we generalize to two points? And how do
we get the probability that it is there at a given time?

If we have psi(x,t),
solution of the Schroedinger equation,

Time dependent or time-independent Schroedinger equation? That is, are you using
the Schroedinger represenation or Heisenberg? I always assumed to do this right,
you have to use Heisenberg, so that when you write the position operator, you
have time as a variable too, to get an expression for the probability that the
electron is at two different given points at the same time. But by writing
psi(x,t), you seem to be assuming Schroedinger.

Then again, this may just reflect how rusty I am at these calculations:(

[snip]


Schwinger + electron + point particle is enough to search on. Thanks, and=
=20
I'll let you know if I find something.

I look forward to seeing it.

[snip]

.

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