Numerical Solution of the two-dimensional time independent Schroedinger Equation by symplectic schemes based on Magnus Expansion

摘要

The solution of the two-dimensional time-independent Schroedinger equation is considered by partial discretisation. The discretized problem is treated as an ordinary differential equation problem and solved numerically by symplectic methods based on Magnus expansion. The problem is then transformed into an algebraic eigenvalue problem involving real, symmetric matrices.