  Coherent states of the two dimensional harmonic oscillator are constructed as
superpositions of energy and angular momentum eigenstates. It is shown that
these states are Gaussian wave-packets moving along a classical trajectory,
with a well defined elliptical polarization. They are coherent correlated
states with respect to the usual cartesian position and momentum operators. A
set of creation and annihilation operators is defined in polar coordinates, and
it is shown that these same states are precisely coherent states with respect
to such operators.
