Talk:Ring wave guide
|WikiProject Physics||(Rated Redirect-class)|
I think you will find that for a "particle in a ring" that the energies are actually
E = (n^2 h^2)/(2 m L^2) L is the length of the ring (ie. 2 pi r)
wavefunctions sin (n*theta) and cos (n*theta) work nice. n is the quantum number and theta the angular displacement round the ring (radians).
apart from the lowest energy level (where only a cos function is allowed - psi squared would be zero for sin) each level is doubly degenerate corresponding to wavefunctions sin and cosine. (or if you want to make it difficult the linear combinations of these... e^-ix and e^+ix). So the first level can hold one particle and all the rest two. The case of electrons in aromatic structures is different as electrons form pairs and so each level will hold an electron pair. Both eenergies and electron densities agree very well with more complex treatments of bonding in these molecules in the ground state. However the wheels fall off to a certain extent for excited states because of symmetry considerations (the ground state is totallly symmetric so there is no problem).
The article badly needs rewriting so that it gives a context and is readable by non-experts. I'm sure it contains a good deal of useful information, but it needs to be explained in a way that the average reader has an outside chance of learning something from it. Tannin 19:33 Apr 4, 2003 (UTC)