  We quantize three Friedmann-Robertson-Walker models in the presence of a
negative cosmological constant and radiation. The models differ from each other
by the constant curvature of the spatial sections, which may be positive,
negative or zero. They give rise to Wheeler-DeWitt equations for the scale
factor which have the form of the Schroedinger equation for the quartic
anharmonic oscillator. We find their eigenvalues and eigenfunctions by using a
method first developed by Chhajlany and Malnev, and use the eigenfunctions in
order to construct wave packets for each case and evaluate the time-dependent
expected value of the scale factors. We find for all of them that the expected
values of the scale factors oscillate between maximum and minimum values. Since
the expectation values of the scale factors never vanish, we conclude that
these models do not have singularities.
