h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I'm in a quantum chemistry class, and our prof used quantum physics to prove that if you have one particle in a box, since the equations he was using are not time-dependent, the particle exists at all points in the box simultaneously. Ignoring that for the moment, we used Hamiltonian physics to derive this equation:
Phi=sqrt(2/L)sin(Pi*x/L) where the particle is in a one-dimensional box of length L. If n=1, Phi vs. x is a sine curve with a maximum at L/2. Now, even though according to the prof Phi has no actual physical meaning, Phi^2 is the probability density of the particle. So this means that the probability of the particle is highest in the middle of the box. In class, I asked my prof whether this implies that if you had multiple particles they would be concentrated toward the middle of the box. His response was "There's only one particle in the box." So he's not going to be any help. So... if you have a one dimensional box will there be more particles in the middle? I know it's a standing wave and all that, I just want to know how this relates to reality.

how can you only have one particle in the box???

i thought that bloody cat was in the box?????

Ha, thanks, I'll have to remember that for the midterm.

How can a box be one dimensional? *resisting rooting out copies of Flatland and Sphereland*

*is bemused that Firefox recognizes Flatland and not Sphereland*

Two particles in a box:

http://www.nyu.edu/classes/tuckerman/honors.chem/lectures/lecture_7/node3.html

" ... there is zero probability to find both particles in small regions near the same point." So it is unlikely that both particles will be in the middle.

isn't this hiezenberg????

policeman: scuse me sir, do you know how fast you were going???

physisist: no! but i knew exactly where i was!!!!

The model he uses is solvable because it is one particle. So it two but it is more complex as the particles will (assuming same charge) repel one another.

Put three in there and it's a three body problem and you get the really interesting stuff in quantum theory - it's not solvable mathematically (too many variables with not enough knowns) and one starts having to use assumptions and approximations.

When you put two particles in the box, you 've a completely different set of equations, and you have to solve it separately and find out what happens. It's not really possible to work it out from the one particle example.

Orcus, obligatory xkcd posting:
http://xkcd.com/613/

Although strictly speaking I think it's a mathematics problem meself

Okay, thanks everyone!! I'll survive this class somehow...

Abtruse goose does a nice line in geek strips these days too...certainly not a copy of xc-whatever.

http://abstrusegoose.com/28

and the archives:

http://abstrusegoose.com/archives