  In this work we show how to complete some Hamilton-Jacobi solutions of
linear, nonconservative classical oscillatory systems which appeared in the
literature and we extend these complete solutions to the quantum mechanical
case. In addition, we get the solution of the quantum Hamilton-Jacobi equation
for an electric charge in an oscillating pulsing magnetic field. We also argue
that for the case where a charged particle is under the action of an
oscillating magnetic field, one can apply nuclear magnetic resonance techniques
in order to find experimental results regarding this problem. We obtain all
results analytically, showing that the quantum Hamilton-Jacobi formalism is a
powerful tool to describe quantum mechanics.
