% the proposal is in plain TeX!

\magnification\magstep1
\nopagenumbers
\parskip=1cm

\font\head=pncb scaled\magstep3
\font\tll=pncr scaled\magstep2
\font\tlb=pncb scaled\magstep2
\font\tlc=pncb scaled\magstep0
\font\tx=pncr at 10pt
\tx
\baselineskip=1.8\baselineskip

\ 
\vfill

\centerline{\head Semiclassical Propagation}\vskip.3cm
\centerline{\head in Smooth Chaotic Potentials}
%\vskip.1cm
%\centerline{\tlc Thesis proposal}
\vskip1cm
\centerline{\tll Albert Dvornik}

\vskip2cm

The proposed thesis would examine semiclassical propagation of
Gaussian wave packets in smooth two-dimensional potentials.  The main
part of the project involves numerical calculations of semi-classical
propagation using Wigner density matrices.  The benefit of using a
time-dependent approach lies in its similarity to modelling
particle propagation in classical mechanics.

The results of this approach will be compared to the results obtained
for classical propagation of particles, as well as exact numerical
solutions of the time-dependent Schr\"{o}dinger equation.  The final
goal is to see how the results obtained using Wigner densities
correspond to (and differ from) the classical and quantum-mechanical
results.

\end
