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Computer Physics Communications 175 (2006) 473481 www.elsevier.com/locate/cpc
 

Summary: Computer Physics Communications 175 (2006) 473­481
www.elsevier.com/locate/cpc
On time-step bounds in unitary quantum evolution using the Lanczos method
N. Mohankumar a,
, Scott M. Auerbach b,c
a Radiological Safety Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, India
b Department of Chemistry, University of Massachusetts Amherst, MA 01003, USA
c Department of Chemical Engineering, University of Massachusetts Amherst, MA 01003, USA
Received 29 April 2006; received in revised form 29 April 2006; accepted 8 July 2006
Available online 24 August 2006
Abstract
To solve the non-relativistic time dependent Schrödinger equation using the Lanczos method, Park and Light have provided an approximate
expression for the time step for a given accuracy. We provide an exact expression for the time step in terms of the eigenvalues and eigenvectors
of the resulting tridiagonal matrix. For two test problems, the values of the time step provided by Park and Light differ significantly from the
exact values provided by the present method. We also indicate upper and lower bounds for the time step in terms of the maximum and minimum
eigenvalues. These bounds indicate the possibility of using a new time step given by the geometric mean of the eigenvalues of the tridiagonal
matrix.
© 2006 Elsevier B.V. All rights reserved.
PACS: 02.60.Dc; 02.70.-c
Keywords: Time dependent Schrödinger equation; Quantum dynamics; Wavepackets; Unitary time evolution; Lanczos method and time step

  

Source: Auerbach, Scott M. - Department of Chemistry, University of Massachusetts at Amherst

 

Collections: Chemistry