• search hit 4 of 6
Back to Result List

A spectral method for Schrödinger equations with smooth confinement potentials

Please always quote using this URN:urn:nbn:de:0296-matheon-10610
  • We study the expansion of the eigenfunctions of Schrödinger operators with smooth confinement potentials in Hermite functions; confinement potentials are potentials that become unbounded at infinity. The key result is that such eigenfunctions and all their derivatives decay more rapidly than any exponential function under some mild growth conditions to the potential and its derivatives. Their expansion in Hermite functions converges therefore very fast, super-algebraically.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar
Metadaten
Author:Jerry Gagelman, Harry Yserentant
URN:urn:nbn:de:0296-matheon-10610
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/02/13
Release Date:2012/02/13
Tag:Schrödinger equation; eigenfunctions; spectral approximation
Institute:Technische Universität Berlin
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B65 Smoothness and regularity of solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J10 Schrödinger operator [See also 35Pxx]
41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A25 Rate of convergence, degree of approximation
41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A63 Multidimensional problems (should also be assigned at least one other classification number in this section)
Preprint Number:921
Verstanden ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.