While from their physical interpretation as the eigenvalues of a
physical operator (10) and thus values observed
in physical measurements, it is clear on physical grounds that
the energy eigenvalues
must be real. Nonetheless, it is as useful exercise and a simple
consistency check on our theory to verify mathematically that
the eigenvalues of
(10) are real. The mathematical proof follows directly from the
Hermitianness of the energy operator 
. The proof we give
below is completely general and and may be applied to any Hermitian operator.
