Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 69 Sayı: 1, 441 - 449, 30.06.2020
https://doi.org/10.31801/cfsuasmas.585800

Öz

Kaynakça

  • Albeverio, S. and Leonid, N., Schrödinger operators with nonlocal point interactions, J. Math. Anal. Appl., 332 (2007), 884--895.
  • Albeverio, S. and Kurasov, P., Pseudo-differential operators with point interactions, Lett. Math. Phys., 41 (1997). 79-92.
  • Allahverdiev, B., Bairamov, E. and Ugurlu, E., Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions, J. Math. Anal. Appl., 401 (2013), 388--396.
  • Bainov, D.D. and Simeovov, P.S., Impulsive differential equations asymptotic properties of the solutions, World Scentific, Singapore, 1995.
  • Bainov, D.D. and Simeovov, P.S., Oscilation theory of impulsive differential equations, International Publications, Orlando, 1998.
  • Bairamov, E. and Ugurlu, E., Krein's theorems for a dissipative boundary value transmission problem, Complex Anal. Oper. Theory, 4 (2013), 831-842.
  • Bakhrakh, V. L. and Vetchinkin, S. I., Green's functions of the Schrödinger equation for the simplest systems, Theor. Math. Phys., 6:3 (1971), 283-290.
  • Benehohra, M., Henderson, J. and Ntouyas, S., Impulsive differential equations and inclusions, Hindawi Publishing Corporation, New York, 2006.
  • Courant, R. and Hilbert, D., Methoden der Mathematischen Physik, Springer, Berlin, 1937.
  • Coutinho, F.A.B., Nogami, Y. and Tomio, L. Many-body system with a four-parameter family of point interactions in one dimension, J. Phys. A. Math. Gen., 32, (1999).
  • Coutinho, F.A.B., Nogami, Y. and Perez, J.F., Generalized point interactions in one-dimensional quantum mechanics, J. Phys. A. Math. Gen., 30 (1997), 3937-3945.
  • Dehghani, I. and Akbarfam, A.J., Resolvent operator and self-adjointness of Sturm-Liouville operators with a finite number of transmission conditions, Mediterr. J. Math., 11 (2014), 447.
  • Marchenko, V.A., Sturm-Liouville operators and applications, Birkhöuser, Basel, 1986.
  • Nenov, S.I., Impulsive controllability and optimization problems in population dynamics, Nonlinear Anal., 36 (1999), 881-890.
  • Sakurai, J.J., Modern Quantum Mechanics, MA, Addison-Wesley, 1985.
  • Tsaur, G. and Wang, J., Constructing Green functions of the Schrödinger equation by elementary transformations, Am. J. Phys. 74 (2006), 600.
  • Ugurlu, E. and Bairamov, E., Spectral analysis of eigenparameter dependent boundary value transmission problems, J. Math. Anal. Appl., 1 (2014) , 482-494.
  • Ugurlu, E. and Bairamov, E., The spectral analysis of a nuclear resolvent operator associated with a second order dissipative differential operator. Comput. Methods Funct. Theory, 17(2) (2016).
  • Yildirim, E., Bound states and spectral singularities of an impulsive Schrödinger equation, Turk. J. Math., 42 (2018), 1670-1679.
  • Zhang, X. and Sun, J., Green function of fourth-order differential operator with eigenparameter-dependent boundary and transmission conditions,Acta Math. Appl. Sin. Engl. Ser., 33 (2017), 311.

Green function and resolvent operator of a Schrödinger equation with general point interaction

Yıl 2020, Cilt: 69 Sayı: 1, 441 - 449, 30.06.2020
https://doi.org/10.31801/cfsuasmas.585800

Öz

In this paper, we investigate the time independent Schrodinger equation which has complex valued potential function under the general point interaction. We construct Green function of this problem and we find the resolvent of the problem in terms of Green function.

Kaynakça

  • Albeverio, S. and Leonid, N., Schrödinger operators with nonlocal point interactions, J. Math. Anal. Appl., 332 (2007), 884--895.
  • Albeverio, S. and Kurasov, P., Pseudo-differential operators with point interactions, Lett. Math. Phys., 41 (1997). 79-92.
  • Allahverdiev, B., Bairamov, E. and Ugurlu, E., Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions, J. Math. Anal. Appl., 401 (2013), 388--396.
  • Bainov, D.D. and Simeovov, P.S., Impulsive differential equations asymptotic properties of the solutions, World Scentific, Singapore, 1995.
  • Bainov, D.D. and Simeovov, P.S., Oscilation theory of impulsive differential equations, International Publications, Orlando, 1998.
  • Bairamov, E. and Ugurlu, E., Krein's theorems for a dissipative boundary value transmission problem, Complex Anal. Oper. Theory, 4 (2013), 831-842.
  • Bakhrakh, V. L. and Vetchinkin, S. I., Green's functions of the Schrödinger equation for the simplest systems, Theor. Math. Phys., 6:3 (1971), 283-290.
  • Benehohra, M., Henderson, J. and Ntouyas, S., Impulsive differential equations and inclusions, Hindawi Publishing Corporation, New York, 2006.
  • Courant, R. and Hilbert, D., Methoden der Mathematischen Physik, Springer, Berlin, 1937.
  • Coutinho, F.A.B., Nogami, Y. and Tomio, L. Many-body system with a four-parameter family of point interactions in one dimension, J. Phys. A. Math. Gen., 32, (1999).
  • Coutinho, F.A.B., Nogami, Y. and Perez, J.F., Generalized point interactions in one-dimensional quantum mechanics, J. Phys. A. Math. Gen., 30 (1997), 3937-3945.
  • Dehghani, I. and Akbarfam, A.J., Resolvent operator and self-adjointness of Sturm-Liouville operators with a finite number of transmission conditions, Mediterr. J. Math., 11 (2014), 447.
  • Marchenko, V.A., Sturm-Liouville operators and applications, Birkhöuser, Basel, 1986.
  • Nenov, S.I., Impulsive controllability and optimization problems in population dynamics, Nonlinear Anal., 36 (1999), 881-890.
  • Sakurai, J.J., Modern Quantum Mechanics, MA, Addison-Wesley, 1985.
  • Tsaur, G. and Wang, J., Constructing Green functions of the Schrödinger equation by elementary transformations, Am. J. Phys. 74 (2006), 600.
  • Ugurlu, E. and Bairamov, E., Spectral analysis of eigenparameter dependent boundary value transmission problems, J. Math. Anal. Appl., 1 (2014) , 482-494.
  • Ugurlu, E. and Bairamov, E., The spectral analysis of a nuclear resolvent operator associated with a second order dissipative differential operator. Comput. Methods Funct. Theory, 17(2) (2016).
  • Yildirim, E., Bound states and spectral singularities of an impulsive Schrödinger equation, Turk. J. Math., 42 (2018), 1670-1679.
  • Zhang, X. and Sun, J., Green function of fourth-order differential operator with eigenparameter-dependent boundary and transmission conditions,Acta Math. Appl. Sin. Engl. Ser., 33 (2017), 311.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik
Bölüm Research Article
Yazarlar

Emel Yıldırım 0000-0002-9894-2113

Yayımlanma Tarihi 30 Haziran 2020
Gönderilme Tarihi 2 Temmuz 2019
Kabul Tarihi 15 Ekim 2019
Yayımlandığı Sayı Yıl 2020 Cilt: 69 Sayı: 1

Kaynak Göster

APA Yıldırım, E. (2020). Green function and resolvent operator of a Schrödinger equation with general point interaction. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 441-449. https://doi.org/10.31801/cfsuasmas.585800
AMA Yıldırım E. Green function and resolvent operator of a Schrödinger equation with general point interaction. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Haziran 2020;69(1):441-449. doi:10.31801/cfsuasmas.585800
Chicago Yıldırım, Emel. “Green Function and Resolvent Operator of a Schrödinger Equation With General Point Interaction”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, sy. 1 (Haziran 2020): 441-49. https://doi.org/10.31801/cfsuasmas.585800.
EndNote Yıldırım E (01 Haziran 2020) Green function and resolvent operator of a Schrödinger equation with general point interaction. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 441–449.
IEEE E. Yıldırım, “Green function and resolvent operator of a Schrödinger equation with general point interaction”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 69, sy. 1, ss. 441–449, 2020, doi: 10.31801/cfsuasmas.585800.
ISNAD Yıldırım, Emel. “Green Function and Resolvent Operator of a Schrödinger Equation With General Point Interaction”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (Haziran 2020), 441-449. https://doi.org/10.31801/cfsuasmas.585800.
JAMA Yıldırım E. Green function and resolvent operator of a Schrödinger equation with general point interaction. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:441–449.
MLA Yıldırım, Emel. “Green Function and Resolvent Operator of a Schrödinger Equation With General Point Interaction”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 69, sy. 1, 2020, ss. 441-9, doi:10.31801/cfsuasmas.585800.
Vancouver Yıldırım E. Green function and resolvent operator of a Schrödinger equation with general point interaction. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):441-9.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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