Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces

ERMAN, FATİH

Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces

Fatih ERMAN (İzmir Yüksek Teknoloji Enstitüsü, Fen Fakültesi, Matematik Bölümü, İzmir, Türkiye)

Turkish Journal of Physics

0 0

Yıl: 2016 Cilt: 40 Sayı: 3 Sayfa Aralığı: 316 - 323 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces

Öz:

In this short article, we nonperturbatively derive a recursive formula for the Green's function associatedwith nitely many point Dirac delta potentials in one dimension. We extend this formula to the one for the Diracdelta potentials supported by regular curves embedded in two-dimensional manifolds and for the Dirac delta potentialssupported by two-dimensional compact manifolds embedded in three-dimensional manifolds. Finally, this formulationallows us to nd the recursive formula of the Green's function for the point Dirac delta potentials in two- and three-dimensional Riemannian manifolds, where the renormalization of coupling constant is required.

Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1]Demkov, Yu. N.; Ostrovskii, V. N.Zero-range Potentials and Their Applications in Atomic Physics, Plenum Press:New York, NY, USA, 1988.
[2]Belloni, M.; Robinett, R. W.Phys. Rep.2014,540, 25-122.
[3]Albeverio, S.; Gesztesy, F.; Hoegh-Krohn, R.; Holden, H.Solvable Models in Quantum Mechanics, 2nd ed; AMS:Chelsea, RI, USA, 2004.
[4]Jackiw, R.Delta-Function Potentials in Two- and Three-Dimensional Quantum Mechanics, M. A. B. Beg MemorialVolume; World Scienti c: Singapore, 1991.
[5]Besprosvany, J.Phys. Rev. B2001,63, 233108.
[6]Kaynak, B. T.; Turgut, O. T.J. Phys. A: Math. Theor.2012,45, 265202.
[7]Kaynak, B. T.; Turgut, O. T.Ann. Phys.2013,339, 266-292.
[8]Exner, P.; Ichinose, T.J. Phys. A: Math. Gen.2001,34, 1439.
[9]Appel, W.Mathematics for Physics and Physicists, Princeton University Press: Princeton, NJ, USA, 2007.
[10]Erman, F.; Turgut, O. T.J. Math. Phys.2006,47, 082110.323

APA	ERMAN F (2016). Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces. , 316 - 323.
Chicago	ERMAN FATİH Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces. (2016): 316 - 323.
MLA	ERMAN FATİH Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces. , 2016, ss.316 - 323.
AMA	ERMAN F Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces. . 2016; 316 - 323.
Vancouver	ERMAN F Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces. . 2016; 316 - 323.
IEEE	ERMAN F "Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces." , ss.316 - 323, 2016.
ISNAD	ERMAN, FATİH. "Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces". (2016), 316-323.

APA	ERMAN F (2016). Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces. Turkish Journal of Physics, 40(3), 316 - 323.
Chicago	ERMAN FATİH Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces. Turkish Journal of Physics 40, no.3 (2016): 316 - 323.
MLA	ERMAN FATİH Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces. Turkish Journal of Physics, vol.40, no.3, 2016, ss.316 - 323.
AMA	ERMAN F Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces. Turkish Journal of Physics. 2016; 40(3): 316 - 323.
Vancouver	ERMAN F Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces. Turkish Journal of Physics. 2016; 40(3): 316 - 323.
IEEE	ERMAN F "Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces." Turkish Journal of Physics, 40, ss.316 - 323, 2016.
ISNAD	ERMAN, FATİH. "Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces". Turkish Journal of Physics 40/3 (2016), 316-323.