On the quantisation of dissipative systems

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Two methods of quantisation of dissipative systems are considered. It is shown that the phase space description of quantum mechanics permits computational simplification, when Kanai’s method is adopted. Since the Moyal Bracket is the same as the Poisson Bracket, for systems described by a most general explicitly time dependent quadratic Lagrangian, the phase space distribution can be obtained as the solution of the corresponding classical Langevin equations in canonical variables, irrespective of the statistical properties of the noise terms. This result remains true for arbitrary potentials too in an approximate sense. Also analysed are Dekker’s theory of quantisation, violation of uncertainty principle in that theory and the reason for the same.