Communications in Mathematical Sciences

Volume 5 (2007)

Number 4

Construction and validation of a rigorous surface hopping algorithm for conical crossings

Pages: 789 – 814



Caroline Lasser

Torben Swart

Stefan Teufel


This article presents and evaluates a surface hopping algorithm for time-dependent two-level Schrödinger systems with conically intersecting eigenvalues. The algorithm implements an asymptotic semigroup for approximating the solution's Wigner function, which was rigorously defined and derived from the Schrödinger equation by two of the authors in previous work. It is applied to two-dimensional isotropic systems, which include linear Jahn-Teller Hamiltonians and Gaussian initial data. It reproduces energy level populations and expectation values with an accuracy of two to three percent.


time-dependent Schrödinger system; eigenvalue crossing; trajectory surface hopping algorithm

2010 Mathematics Subject Classification

65Z05, 81-04

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