A Relaxation Method for Nonlocal and Non-Hermitian Operators

Authors: Lagaris I.E.; Papageorgiou D.G.; Braun M.; Sofianos S.A.

Source: Journal of Computational Physics, Volume 126, Number 1, June 1996 , pp. 229-236(8)

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Abstract:

We present a grid method to solve the time dependent Schrodinger equation (TDSE). It uses the Crank-Nicholson scheme to propagate the wavefunction forward in time and finite differences to approximate the derivative operators. The resulting sparse linear system is solved by the symmetric successive overrelaxation iterative technique. The method handles local and nonlocal interactions and Hamiltonians that correspond to either Hermitian or to non-Hermitian matrices with real eigenvalues. We test the method by solving the TDSE in the imaginary time domain, thus converting the time propagation to asymptotic relaxation. Benchmark problems solved are both in one and two dimensions, with local, nonlocal, Hermitian and non-Hermitian Hamiltonians.

Language: English

Document Type: Research article

Affiliations: Physics Department, University of South Africa, Pretoria, 0001, South Africa

Publication date: 1996-06-01