Green's Function for A Piecewise Continous Potential via Integral Equations Method

Benali Brahim; Mohammed Tayeb Meftah; Rai Vandana

doi:10.22342/jims.24.2.387.20-35

Benali Brahim ⁽¹⁾ , Mohammed Tayeb Meftah ⁽²⁾ , Rai Vandana ⁽³⁾

(1) el-oued university, Algeria,

(2) ,

(3)

https://doi.org/10.22342/jims.24.2.387.20-35

Issue
Volume 24 Number 2 (October 2018)

Submitted
December 22, 2016

Accepted
February 20, 2018

Published
May 18, 2018

Keywords:

integral equations and Green Kernel and Bessel Transformation,

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Abstract

The aim of this work is to provide Green's function for the Schrodingerequation. The potential part in the Hamiltonian is piecewise continuous operator.It is a zero operator on a disk of radius "a" and a constant V0 outside this disk (intwo dimensions). We have used, to construct the Green's function, the technique ofthe integral equations. We have respected the boundary conditions of the problem.The discrete spectra of the Hamiltonian operator have been also derived.

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References

Melnikov Y. A., On a Test and planar movment Eng. Anal. Bound. Elem. 25 669{676 (2001).

Ben Ali B and Meftah M.T., Explicit quantum Green's functions on a piecewise continuous

symmetrical spherical potential Rep. Math. Phys. 74 73-87 (2014).

Kukla S., Siedlecka U. and Zamorska I., On a Test and planar movments, Sci. Res. Inst. Math.

Computer Sci. 11 (1), 53 (2012).

Kukla S., On a Test and planar movment alone x, Sci. Res. Inst. Math. Computer Sci. 9 (1),

(2010).

Adhikari S. K.: Am. J. Phys. 54 362367 (1986).

Nemenman I. M.,Silbergleit A. S.: J. Appl. Phys. 86, No. 1 614624 (1999).

Yoshio Nosaka J.: Phys. Chem. 95 50545058 (1991).

Layeghnejad R., Zare M. and Moazzemi R.: Phys. Rev. D 84 125026 (2011).

Tago Y., Narasimha K.: Phys. Lett. 45A, No. 1 3738 (1973).

Berezin F. A. and Shubin M. A. The Schroedinger Equation. Kluwer Academic Publishers,

Feynman R. P. and Hibbs A. R.: Quantum Mechanics and Path Integrals (1965) (New York:

McGraw Hill).

Authors

Benali Brahim

el-oued university

benalibrahim@ymail.com (Primary Contact)

Mohammed Tayeb Meftah

Rai Vandana

Author Biography

Benali Brahim, el-oued university

el-oued 39000

Brahim, B., Meftah, M. T., & Vandana, R. (2018). Green’s Function for A Piecewise Continous Potential via Integral Equations Method. Journal of the Indonesian Mathematical Society, 24(2), 20–35. https://doi.org/10.22342/jims.24.2.387.20-35