Generalized spectrum approximation and numerical computation of eigenvalues for Schrödinger’s operators
Tóm tắt
We show that the spectrum of a Schrödinger’s operator is equal to the generalized spectrum of two bounded operators. Using an approximation method of integral operator, based on regularization by convolution and Fourier series, we approach perfectly the spectrum of the harmonic oscillator.
Tài liệu tham khảo
E. B. Davies, J. Operator Theory 43, 243 (2000).
H. Guebbai and A. Largillier, Spectra and Pseudospectra of Convection-Diffusion Operator (Accepted in Lobachevskii Journal ofMathematics 2012).
T. Kato, Perturbation Theory of Linear Operators (Springer-Verlag, Berlin, Heidelberg and New York, 1980).
M. Ahues, A. Largillier, and B. V. Limaye, Spectral Computations for Bounded Operators (Chapman and Hall/CRC, New York, 2001).
A. J. Laub, Matrix Analysis for Scientists and Engineers (SIAM, California, 2005).
G. F. Roach, Green’s Functions (Cambridge University Press, New York, 1982).
H. Guebbai, Regularization and Fourier Series for Fredholm Integral Equations of the Second Kind with A Weakly Singular Kernel, (submitted to AppliedMathematic Letter 2011).
L. Boulton, J. Operator Theory 47, 413 (2002).
E.B. Davies and M. Plum, Spectral Pollution, arXiv:math/0302145v1, (2002)
E. Shargorodsky, Bull. London Math. Soc. 41, 524 (2009).
S. Roch and B. Silbermann, J. Operator Theory 35, 241 (1996).
D. F. Griffiths and G. A. Watson, Numerical Analysis (Longman Sci. Tech. Publ., Harlow, UK, 1992).
L. N. Trefethen, SIAM Review 39, 383 (1997).
R. A. Adams, Sobolev Spaces (Academic Press, New York, 1975).
integrals.wolfram.com.