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A nonlinear quantum-classical transition wave equation is proposed fordissipative systems within the Caldirola-Kanai model. Equivalence of thistransition equation to a scaled Schr\"{o}dinger equation is proved. Thedissipative dynamics is then studied in terms of what we call scaledtrajectories following the standard procedure used in Bohmian mechanics. Thesetrajectories depend on a continuous parameter allowing us a smooth transitionfrom Bohmian to classical trajectories. Arrival times and actual momentumdistribution functions are also analyzed. The propagation of a Gaussian wavepacket in a viscid medium under the presence of constant, linear and harmonicpotentials is studied. The gradual decoherence process and localization areeasily visualized and understood within this theoretical framework.

Quantum-classical transition in dissipative systems through scaled trajectories