Quantum theory of nonconservative systems

Abstract

We present here in a systematic way a reformulation and a generalization of a quantum theory of nonconservative (dissipative and antidissipative) systems already outlined by us many years ago. In particular, following a procedure first introduced by Levi Civita we give a detailed formulation of the corresponding classical Lagrangian and Hamiltonian treatments and consequently we show that quantum nonconservative systems can be equivalently described by the Schrodinger or Heisenberg picture. Furthermore, a detailed discussion of uncertainty rules for nonconservative systems is developed. By means of such a formulation it is possible to overcome easily criticisms raised against the so-called Caldirola-Kanai equation. Finally the connection between the Schrodinger equation for nonservative systems and the master equation is shortly discussed and some new possible developments of the theory are suggested.