  In continuation of our previous work investigating the possibility of the use
of the Level Set Method in quantum control, we here present some numerical
results for a Morse potential. We find that a proper treatment of the Morse
potential eigenfunctions and eigenvalues for the case of a system with a small
number of bound energy levels, the anharmonic perturbative approximation is
actually invalid. We, therefore, use a Runge-Kutta integration method that
gives more plausible results. We also calculate the dipole moment for the
transitions between the two levels with our eigenfunctions and find that there
is a critical depth of the potential. Finally we find the level sets giving
equal expectation values of the energy, and comment on the unitary operators
needed to make transitions from any level set to another.
