Solution of time-independent Schrödinger equation by the imaginary time propagation method

Authors:
L. Lehtovaara;J. Toivanen;J. Eloranta
Affiliations:
Department of Chemistry, University of Jyväskylä, Survontie 9, 40500 Jyväskylä, Finland;Center for Research in Scientific Computation, Box 8205, North Carolina State University, Raleigh, NC 27695-8205, USA;Department of Chemistry, University of Jyväskylä, Survontie 9, 40500 Jyväskylä, Finland and Department of Chemistry and Biochemistry, California State University Northridge, No ...
Venue:
Journal of Computational Physics
Year:
2007

Citing 3
Cited 3

Numerical recipes in C (2nd ed.): the art of scientific computing

Numerical recipes in C (2nd ed.): the art of scientific computing
Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
Efficient numerical method for simulating static and dynamic properties of superfluid helium

Journal of Computational Physics

Multilayer perceptron neural networks with novel unsupervised training method for numerical solution of the partial differential equations

Applied Soft Computing
Numerical methods for computing ground states and dynamics of nonlinear relativistic Hartree equation for boson stars

Journal of Computational Physics
A hybrid discontinuous Galerkin method for computing the ground state solution of Bose-Einstein condensates

Journal of Computational Physics

Quantified Score

Hi-index	31.46

Visualization

Abstract

Numerical solution of eigenvalues and eigenvectors of large matrices originating from discretization of linear and non-linear Schrodinger equations using the imaginary time propagation (ITP) method is described. Convergence properties and accuracy of 2nd and 4th order operator-splitting methods for the ITP method are studied using numerical examples. The natural convergence of the method is further accelerated with a new dynamic time step adjustment method. The results show that the ITP method has better scaling with respect to matrix size as compared to the implicitly restarted Lanczos method. An efficient parallel implementation of the ITP method for shared memory computers is also demonstrated.