ON A LOGARITHMIC NONLINEAR SCHRÖDINGER EQUATION COMPATIBLE WITH HADRONIC MECHANICS AND ITS CONNECTION WITH OTHER APPROACHES FOR THE DESCRIPTION OF DISSIPATIVE SYSTEMS.

The time-dependent approach of Caldirola and Kanai (CK) for dissipative systems can be traced back to the conventional system-plus-reservoir approach; however, it apparently violates the uncertainty principle. This discrepancy can be avoided by considering a consistent transition between the CK formalism and a logarithmic nonlinear Schrödinger equation (NLSE) which requires not only a transformation of the operators, but also a nonunitary transformation of the wave function. This procedure also shows the equivalence of three approaches which, at first sight, seem to be incompatible with each other for the description of dissipative quantum systems. In addition, the transition from the NLSE to the linear canonical CK-theory presents an explicit example of genolinearization, introduced by R.M. Santilli in the framework of hadronic mechanics. [ABSTRACT FROM AUTHOR]