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

Benali Brahim, Mohammed Tayeb Meftah, Rai Vandana


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.


integral equations and Green Kernel and Bessel Transformation:

Full Text:



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),


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).



  • There are currently no refbacks.

Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
Senolowo, Sinduadi, Mlati, Sleman Regency, Special Region of Yogyakarta 55281, Telp. (0274) 552243

p-ISSN: 2086-8952 | e-ISSN: 2460-0245

Journal of the Indonesian Mathematical Society is licensed under a Creative Commons Attribution 4.0 International License

web statistics
View My Stats