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The T.M. Field
For the T.M. degrees of freedom the source and the electromagnetic
field are also derived from a solution to the same inhomogeneous
scalar wave Eq.(5). However, the difference
from the T.E. case is that the fourvector components of the source and
the vector potential lie in the Lorentz plane. Thus, instead
of Eqs.(9) and (10), one has the T.M. source

(11) 
and the T.M. vector potential

(12) 
All the corresponding T.M. field components are derived from the
scalar :

(13) 
These components are guaranteed to satisfy all the Maxwell field equations
with the T.M. source, Eq.(11), whenever
satisfies the inhomogeneous scalar wave equation, Eq.(5).
Ulrich Gerlach
20011009