Green Function on a Quantum Disk for the Helmholtz Problem

• Authors: B. Benali , B. Boudjedaa , M. Meftah
• 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

EN

03.75.Lm; 03.65.Db; 02.30.Gp; 02.30.Sa

Discipline

• 03.75.Lm: Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations(see also 74.50.+r Tunneling phenomena; Josephson effects in superconductivity)
• 03.65.Db: Functional analytical methods
• 02.30.Sa: Functional analysis
• 02.30.Gp: Special functions

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2013
• Volume: 124
• Issue: 4
• Pages: 636-640

Dates

published

2013-10

received

2013-03-09

(unknown)

2013-05-17

Contributors

author

B. Benali

• Mathematical Department, Biskra University, 07000 and El-Oued University, 39000, Algeria

author

B. Boudjedaa

• Mathematical Department, Jijel University, 18000, Algeria

author

M. Meftah

• 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)

Identifiers

DOI

10.12693/APhysPolA.124.636