Re: Fermions

In article <87slpisegh.fsf@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Henning Makholm <henning@xxxxxxxxxxx> wrote:
Scripsit glhansen@xxxxxxxxxxxxxxxxxxxxx (Gregory L. Hansen)
Henning Makholm <henning@xxxxxxxxxxx> wrote:

The archetypical massive boson, if many popular texts are to be
believed, is the He-4 atom. Being bosons means that two He-4 atoms are
allowed to occupy the same state simultaneously. But these atoms have
internal parts, so if two atoms are in the same states, then e.g. the
spin-up electron in one atom must be in the same state as the spin-up
electron in the other atom. And _electrons_ are not allowed to do
that. An apparent paradox.

In the first paragraph you seem to forget that there's another quantum
number involved-- which atom is the electron associated with? Both
electrons can be in the n=0, S=0 state if one is associated with atom one
and the second is associated with atom two.

I think that this solution amounts to begging the question. - At least
it begs the question I was trying to express: The electron, by itself,
knows nothing of atoms - how can it know that it is supposed to behave
as if it had a "which atom" quantum number? Or in other words, how can
it be that the approximation where we asign electrons to particular
atoms is even approximately valid compared to what we'd get if we just
wrote down the Schrödinger equation for two alpha particles and four
electrons and investigated from first principles what would happen
then? The Schrödinger equation certainly don't presuppose any atomic
quantum numbers; rather it is supposed to _explain_ them.

Both electrons might be in 1S spin up states, but one has a 1S spin up
state that centered over here, and the other as a 1S spin up state that's
centered over there. Not the same state.


Of course I'm not sure that the 18-dimensional case of 2 alpha + 4 e
is tractable even numerically, but if I manage to learn how to write
it down in the first place I might try to see which understanding
numeric solutions of lower-dimensional model systems could lead me to.

That's sort of a half-assed hand-wavy explanation. Ramamurti Shankar
devotes Chapter 10 to multi-particle systems,

I am unfamiliar with "Ramamurti Shankar". Do you have a fuller reference?

Shankar, "Principles of Quantum Mechanics" 2nd ed., Plenum Press, 1994.
--
"Suppose you were an idiot... And suppose you were a member of
Congress... But I repeat myself." - Mark Twain
.

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