On Nelson processes with boundary condition (Q1262630)

In Nelson's stochastic mechanics, quantum phenomena are described in terms of diffusions corresponding to wave functions \(\psi\) (x,t), \((x,t)\in R^ n\times [0,\infty),\) which are the solutions of Schrödinger equations \(i(\partial \psi /\partial t)=H \psi,\) with \(H=- \Delta +V\). In this article, for the solutions of Schrödinger equations on bounded intervals, the existence of corresponding conservative diffusions with reflection is shown.