A dynamical system with a damping that is quadratic in velocity is converted into the Hamiltonian format using a nonlinear transformation. Its quantum mechanical behaviour is then analysed by invoking the Gaussian effective potential technique. The method is worked out explicitly for the Duffing oscillator potential.
G. Ambika and Dr. V . M. Nandakumaran, “The quantum effects in quadratically damped systems”, Physics Letters A, vol. 192, pp. 331–336, 1994.