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We present a formalism for which a dissipative system is given by avariational principle. The formalism applies to dynamical systems where itstrajectory is monotonic. Subsequently, we derive its Lagrangian andHamiltonian. From the Hamiltonian, we quantize canonically the classicalparticle in a viscous media. We study the free quantum particle in a viscousmedia and the dissipative quantum tunnelling. It is found that the dissipationinfluences tunnelling probability by a factor that closely resembles the resultof Caldeira and Leggett.

Canonical Quantization Approach of a Class of a Dissipative System: Applications to Quantum Tunnelling with Dissipative Coupling