Re: [Phys-l] spherical waves

[David Bowman <David_Bowman@georgetowncollege.edu>]

Oops. In my response to Kyle I advertantly left off a condition defining EM waves in my last post.  I forgot to mention the *tranversality* of the waves when describing EM vector waves.

I wrote:

> ....
> For EM waves the monopole spherically symmetric L=0 solution is
> not allowed because they are vector waves, not scalar waves,
> and have no spherically symmetric solution.  (Think of trying
> to comb the hair on a hairy sphere).  The lowest order
> multipole solution has L = 1 (i.e. the angular symmetry of a
> chemist's p-orbital).  ....

But what I ought to have written is:

"For EM waves the monopole spherically symmetric L=0 solution is not allowed because they are *transverse* vector waves, not scalar waves, and have no spherically symmetric solution.  (Think of trying to comb the hair on a hairy sphere).  The lowest order multipole solution has L = 1 (i.e. the angular symmetry of a chemist's p-orbital)."

It is the transversality of the EM waves that forbids the spherically symmetric solution.  It is possible to have a *longitudinal* spherically symmetric vector wave, just not a transverse one.  (For a longitudial spherically symmetric wave the hair on the hairy sphere stands up on end locally perpendicular to the surface everywhere on it.)

David Bowman