Kernel density estimation-based solution of the nuclear Schrodinger equation

Solving the time-dependent Schrödinger equation for nuclear motion remains a challenge. Despite novel approaches based on Bohmian mechanics, the long-time stability and generalization to multiple dimensions remains an open question. In the present work a method based on an ensemble of classical particles instead of a wave function is employed to evolve the system. Quantum effects are introduced through forces derived from the quantum potential Q and the necessary derivatives are obtained from a density estimate using kernel density estimation. Application of the procedure to typical 1- and 2-dimensional problems yields good agreement with numerically exact solutions and favourable scaling with the number of particles is found.