Lyonell Boulton and Michael Levitin 2007 J. Phys. A: Math. Theor. 40 9319 doi:10.1088/1751-8113/40/31/010
Lyonell Boulton and Michael Levitin
Show affiliationsThis paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrödinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so-called quadratic projection method, in order to achieve convergence free from spectral pollution. We describe the theoretical foundations of the method in detail and illustrate its effectiveness by several examples.
Issue 31 (3 August 2007)
Received 14 February 2007, in final form 21 June 2007
Published 19 July 2007
Lyonell Boulton and Michael Levitin 2007 J. Phys. A: Math. Theor. 40 9319
Michael Levitin et al 2006 J. Phys. A: Math. Gen. 39 2073
Sylvain Fasel et al 2004 New J. Phys. 6 163
J L Duligall et al 2006 New J. Phys. 8 249
Kedar S Ranade and Gernot Alber 2006 J. Phys. A: Math. Gen. 39 1701
M Khudaverdyan et al 2008 New J. Phys. 10 073023
S Teichmann et al 2009 J. Phys. D: Appl. Phys. 42 135108
C H Wolff et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42 085301
J L Bohn et al 2009 New J. Phys. 11 055039
C E Davis et al 2009 Meas. Sci. Technol. 20 025201