On the Quantum Langevin Equation

Some 20 years ago, in a paper written jointly with Peter Mazur, we presented a discussion of the statistical mechanics of a coupled-oscil lator model of a heat bath. ~1) This model enabled us to obtain the quan tum mechanical form of the Langevin equat ion for a Brownian particle moving in an external potential. Ou r purpose here is to repeat this derivation, using a different, some would say simpler, oscillator model of the heat bath. Repeating the discussion will enable us to lay a different emphasis on certain aspects of the derivation and of the equat ion itself, aspects that have become of interest in the intervening years. As in our earlier paper, for simplicity we restrict our considerations to a particle moving in one dimension; it will be seen that this is not an essential restriction. In this case the quan tum Langevin equat ion is the (Heisen-