The generalized Schrödinger–Langevin equation

Antonio Boulhosa Nassar

Roland Katz, Pol-Bernard Gossiaux

Manuel O. Cáceres, Ana Karina Chattah

Jairo Alonso Mendoza Suárez, Juan Carlos López-Carreño, Rosalba Suarez

Introduction: an alternative solution to the Schrodinger-Langevin equation is presented, where the temporal dependence is explained, assuming a Coulomb potential. Finally, the trajectory equations are found. Objective: in this paper we contribute by presenting a detailed and simple solution of the Schrödinger-Langevin equation for a Coulomb potential. Materials and Methods: using an appropriate ansatz, we solve the Schrödinger-Langevin equation, finding the expected values of position and moment. Results: a simple method was presented to find the expected position and moment values in the Schrödinger-Langevin equation, the ansatz used to find these solutions allows the model to be generalized in a certain way to electric potentials and harmonic oscillators. Conclusions: the model used to solve the Schrödinger-Langevin equation, allowed to find the expected values of position and moment of a particle in a Coulomb potential, the temporal dependence of such solutions is made explicit, which allows finding the path equations of the particles.

Crispin W. Gardiner

Antnio B. Nassar

We investigate special types of solutions of the hydrodynamical version of a generalized Schr\"odinger-Langevin equation (GNLSLE), derived in an earlier work, via stochastic mechanics. Within the same scheme of stochastic differential equations, we decompose the stochastic process associated with the GNLSLE into two independent processes: a classical Langevin-type process and a pure quantum Nelson-type process.