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

On the Hamilton-Jacobi method in classical and quantum nonconservative systems