2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140366We study the ergodicity of finite-dimensional approximations of the Schrödinger equation. The system is driven by a multiplicative scalar noise. Under general assumptions over the distribution of the noise, we show that the system has a unique stationary measure $μ$ on the unit sphere $S$ in $\C^n$, and $μ$ is absolutely continuous with respect to the Riemannian volume on $S$. Moreover, for any initial condition in $S$, the solution converges exponentially fast to the measure $μ$ in the variational norm.Mathematical Physicstext