A random walk model for the Schrödinger equation
- Wagner, Wolfgang
2010 Mathematics Subject Classification
- 35Q41 60J25 81Q05
- Schrödinger equation, probabilistic representation, random walk model, piecewise deterministic Markov process
A random walk model for the spatially discretized time-dependent Schrödinger equation is constructed. The model consists of a class of piecewise deterministic Markov processes. The states of the processes are characterized by a position and a complex-valued weight. Jumps occur both on the spatial grid and in the space of weights. Between the jumps, the weights change according to deterministic rules. The main result is that certain functionals of the processes satisfy the Schrödinger equation.
- Math. Comput. Simulation, 143 (2018), pp. 138--148, DOI 10.1016/j.matcom.2016.07.012 .