Re: Elliptical orbits and Sommerfeld

[Jack Uretsky <jlu@HEP.ANL.GOV>]

        Once you've fixed the energy and angular momentum, the orbit is
classical.  You've got to decide what kind of average you are referring
to.  The mean square velocity must be the same as the means square kinetic
energy (up to a factor).  The mean speed can be calculated from the length
of the ellipse and the period, but is not IMO a very interesting number.


On Wed, 30 Jul 2003, Craig Lucanus wrote:

> I have been studying spectroscopy and the development of atomic theory to
> the point where Sommerfeld proposes elliptical electron orbits in atoms. It
> works out that in electron shells represented by principle quantum number
> 'n',  for n>1 there is one circular orbit and one or more elliptical orbits,
> and all orbits in a shell have the same sized diameter(circle) or major
> axis(ellipse). For example, for n=2 there is one circular and one elliptical
> orbit. A question I cannot find an answer to is whether Sommerfeld proposed
> that an electron in the elliptical orbit in the second shell would is move
> with a greater average speed than an electron in the circular orbit.
> It seems to me this it should so as the energies of the electron in either
> orbit is supposed to be to be the same (ie. the energies of the two orbits
> are degenerate) and the average radius of the ellipse must be less than the
> radius of the circle, making the average PE of the elliptically orbiting
> electron less than the circularly orbiting one. Sommerfield proposed a
> relativistic effect upon the electron in the elliptical orbit, due to its
> great speed around perihelion, but is this significant in the whole scheme.
> Anyway, I'll cut to the chase. I'd really appreciate it if somebody tell me
> if I'm on the right track, or direct me to somewhere online I can find
> answers to this questions.

--
  "Don't push the river, it flows by itself"
                                Frederick Perls