Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30184
Very-high-Precision Normalized Eigenfunctions for a Class of Schrödinger Type Equations

Authors: Amna Noreen , Kare Olaussen

Abstract:

We demonstrate that it is possible to compute wave function normalization constants for a class of Schr¨odinger type equations by an algorithm which scales linearly (in the number of eigenfunction evaluations) with the desired precision P in decimals.

Keywords: Eigenvalue problems, bound states, trapezoidal rule, poisson resummation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334948

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2526

References:


[1] A. Mushtaq, A. Noreen, K. Olaussen, and I. ├ÿverb├©, Very-high-precision solutions of a class of Schrdinger type equations, Computer Physics Communications, (in press) doi:10.1016/j.cpc.2010.12.046 (2011)
[2] J. Zinn-Justin, Expansion around instantons in quantum mechanics, J. Math Phys. 22, 511 (1981)
[3] C.M. Bender, K. Olaussen and P.S. Wang, Numerological analysis of the WKB approximation in large order, Physical Review D16, 1740 (1977)
[4] A collection is given in M. Abramowitz and I.A. Stegun, Handbook of mathematical functions, sect. 25.4, Dover Publications, (1970).
[5] Ibid, equation. 25.4.4
[6] ├ÿ. Tafjord, Master thesis, Institutt for fysikk, NTH 1994.
[7] B. Haible and R.B. Kreckel, CLN - Class Library for Numbers, http://www.ginac.de/CLN/