## Preprint 2010-08

## Franco Fagnola, Carlos M. Mora:

### Linear stochastic Schrödinger equations with unbounded coefficients

### Abstract:

We deal with stochastic evolution equations that describe the dynamics of open quantum systems. In particular, we focus on physical systems with infinite dimensional space states such as bosons and atoms. Using resolvent approximations, we obtain a general sufficient condition for the existence and uniqueness of regular solutions to the linear stochastic Schrödinger equations driven by cylindrical Brownian motions. From this we get a new criterion for the existence and uniqueness of weak (probabilistic) regular solutions to the non-linear stochastic Schrödinger equations. These stochastic evolution equations on complex Hilbert spaces govern quantum measurement processes. We apply our results to physical systems involving, essentially, measurements of the position of particles.

This preprint gave rise to the following definitive publication(s):

**Franco FAGNOLA, Carlos M. MORA: ***Linear stochastic Schrödinger equations with unbounded coefficients*. ALEA-Latin American Journal of Probability and Mathematical Statistics, vol. 10, 1, pp. 191-223, (2013).