PL EN


Preferences help
enabled [disable] Abstract
Number of results
2013 | 124 | 4 | 636-640
Article title

Green Function on a Quantum Disk for the Helmholtz Problem

Content
Title variants
Languages of publication
EN
Abstracts
EN
In this work, we present a new result which concerns the derivation of the Green function relative to the time-independent Schrödinger equation in two-dimensional space. The system considered in this work is a quantal particle that moves in an axi-symmetric potential. At first, we have assumed that the potential V(r) to be equal to a constant V_0 inside a disk (radius a) and to be equal to zero outside the disk. We have used, to derive the Green function, the continuity of the solution and of its first derivative, at r=a (at the edge). Secondly, we have assumed that the potential V(r) is equal to zero inside the disk and is equal to V_0 outside the disk (the inverted potential). Here, also we have used the continuity of the solution and its derivative to obtain the associate Green function showing the discrete spectra of the Hamiltonian.
Keywords
Contributors
author
  • Mathematical Department, Biskra University, 07000 and El-Oued University, 39000, Algeria
author
  • Mathematical Department, Jijel University, 18000, Algeria
author
  • Physics Department, LRPPS Laboratory, UKM Ouargla, 30000 Algeria
References
  • [1] Y.A. Melnikov, Eng. Anal. Bound. Elem. 25, 669 (2001)
  • [2] S. Kukla, U. Siedlecka, I. Zamorska, Sci. Res. Inst. Math. Computer Sci. 11 (1), 53 (2012)
  • [3] S. Kukla, Sci. Res. Inst. Math. Computer Sci. 9 (1), 77 (2010)
  • [4] S. Kukla, Sci. Res. Inst. Math. Computer Sci. 11 (1), 85 (2009)
  • [5] S.K. Adhikari, Am. J. Phys. 54, 362 (1986)
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv124n405kz
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.