Re: An electron in a magnetostatic field

On 2006-03-30, Phil Gardner <pej_dg@xxxxxxxxxxx> wrote:
An isolated electron in a magnetostatic field experiences a torque of
magnitude, T = mu x B, which results in precession of the electron's
spin/magnetic axis. It has just one minimum energy state that is
defined by T = 0, mu . B > 0. When in this state there is no lower
energy state to which it can move so it would seem that no radiation
can occur and that this should be true for any electron momentum. This
would seem to offer a simple, physical, classical, explanation of the
existence of stationary, non-radiating states for an electron in
orbital (and thus accelerated) motion as first postulated by Bohr.

Except that the electron in orbital motion is not isolated (it's being
acted on by the nucleus' Coulomb potential). No matter what its magnetic
moment orientation is, a classical electron in orbital motion is still
moving non-uniformly and hence radiating. An electron can always go to
a lower energy state by moving closer to the nucleus.


Is there any existing hard evidence (from experiments with low density
beams of polarised electrons) to the contrary?

To the contrary of what? If contrary to the hypothesis that the Hydrogen
atom is purely classical, then yes there are many. For instance: the
stability of matter.

If not, this "no
precession, no radiation" hypothesis seems to point up a clear
deficiency of Larmor's classical model of radiation by an accelerated
charged particle - its neglect of the particle's magnetic moment.

Perhaps is this hypothesis were correct. However, it doesn't seem to be.
There are definitely corrections to Larmor's formula due to the
electron's magnetic moment, which I'm sure have been taken into account
by those who've come after Larmor. But these corrections will be small.
Consider for example the effect of LS coupling (which is the interaction
of the electron's spin with the magnetic field generated by its orbital
motion) on splitting of the Hydrogen energy levels.

Igor

.

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