Araştırma Makalesi
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PT/non PT Symmetric and non-Hermitian q-deformed Trigonometric Scarf Potential via Path Integral Method

Yıl 2020, , 180 - 184, 30.06.2020
https://doi.org/10.7240/jeps.601583

Öz

In this study,
energy spectrum and corresponding wave function of PT / non PT Symmetric and
Non-Hermitian q-deformation Trigonometric Scarf Potential were obtained by
using Path Integral method. First, the kernel of this potential was derived in terms
of energy spectrum and wave function using parametric time. Energy spectrum and
wave function were shown by Green function obtained from Kernel.

Kaynakça

  • [1] Bender C. M. and Boettcher S. (1998). Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry. Phys. Rev. Lett. 80, 5243.
  • [2] Bender C.M. (2012). PT-symmetric quantum theory. Journal of Physics: Conference Series 63, 012002 .
  • [3] Mostafazadeh A. (2002). Pseudo-Hermiticity versus PT-symmetry. II. A complete characterization of non-Hermitian Hamiltonians with a real spectrum. J. Math. Phys. 43, 2814.
  • [4] L´evai G., Znojil M. (2000). Systematic search for PT symmetric potentials with real energy spectra. J. Phys. A: Math. Gen. 33 , 7165–7180.
  • [5] Feynmann R. and Hibbs A. (2010). Quantum Mechanics and Path Integrals. Emended Edition, Dover Publications Inc. Mineola, New York, 371s.
  • [6] Arai A. 1991). Exactly solvable supersymmetric quantum mechanics. J. Math. Anal Appl., 158, 63-79.
  • [7] Duru I.H., and Kleinert H.(1979). Solution of the path integral for the H-atom. Phys. Lett. B84, 185.
  • [8] Duru I.H. (1983). Morse-potential Green's function with path integrals. Phys. Rev. D, 28, 2689.
  • [9] Grosche C. (2005). Path integral solutions for deformed Poschl-Teller-like and conditionally solvable potentials. J. Phys. A: Math. Gen., 38, 2947-2958.
  • [10] Grosche C. (1989). Path integral solution of a class of potentials related to the Pöschl-Teller potential,. J. Phys. A: Math. Gen., 22, 5073-5087.
  • [11] Kandirmaz N. (2017). PT-/non-PT-Symmetric and Non-Hermitian Generalized Woods-Saxon Potential: Feynman Path Integral Approach GU j Sci.30(1), 133-138.
  • [12] Yesiltas O. (2007). PT/Non-PT Symmetric and Non-Hermitian Poschl-Teller-Like Solvable Potentials via Nikiforov-Uvarov Method. Phys. Scr., 75, 41-46.
  • [13]Alvarez-Castillo D.E. and Kirchbach M. (2007). Exact spectrum and wave functions of the hyperbolic Scarf potential in terms of finite Romanovski polynomials. Revista Mexicana de Fisica, E53(2), 143-154.
  • [14] Falaye, B. J. and Oyewumi, K. J. (2011). Solutions of the Dirac Equation with Spin and Pseudospin Symmetry for the Trigonometric Scarf Potential in D-dimensions. AfricanReview of Physics 6 (0025), 211–220.
  • [15] Suparmi A., Cari C., Deta UA. et al. (2014). Exact Solution of Dirac Equation for q-Deformed Trigonometric Scarf potential with q-Deformed Trigonometric Tensor Coupling Potential for Spin and Pseudospin Symmetries Using Romanovski Polynomial. Journal of Phys. Conference Series,539(2014), 012004.
  • [16] Arda A., Sever R. (2010). Effective-mass Klein–Gordon equation for non-PT/non-Hermitian generalized Morse potential. Phys.Scr., 82(6), 065007.
  • [17] Kandirmaz N., Sever R. (2009). Path Integral Solutions of PT-/Non-PT-Symmetric and Non-Hermitian Morse Potentials. Chinese J. Phys. 47,47.
  • [18] Kandirmaz N., Sever R. (2011). Path Integral Solution of PT-/non-PT-Symmetric and non-HermitianHulthen Potential, Acta Polytechnica, 51, 1.

Path Integral Yöntemiyle PT Simetrik/ PT Simetrik Hermityen Olmayan q-deformasyonlu Trigonometrik Scarf Potansiyeli

Yıl 2020, , 180 - 184, 30.06.2020
https://doi.org/10.7240/jeps.601583

Öz

Bu çalışmada PT Simetrik/ PT
Simetrik Hermityen Olmayan q-deformasyonlu Trigonometrik Scarf Potansiyelinin
enerji spektrumu ve karşılık gelen dalga fonksiyonu Path İntegral yöntemi
kullanılarak elde edildi. Öncelikle bu potansiyelin kerneli parametrik zaman
kullanılarak enerji spektrumu ve dalga fonksiyonu cinsinden türetildi.
Kernelden elde edilen Green fonksiyonu ile enerji spektrumu ve dalga fonksiyonu
gösterildi. 

Kaynakça

  • [1] Bender C. M. and Boettcher S. (1998). Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry. Phys. Rev. Lett. 80, 5243.
  • [2] Bender C.M. (2012). PT-symmetric quantum theory. Journal of Physics: Conference Series 63, 012002 .
  • [3] Mostafazadeh A. (2002). Pseudo-Hermiticity versus PT-symmetry. II. A complete characterization of non-Hermitian Hamiltonians with a real spectrum. J. Math. Phys. 43, 2814.
  • [4] L´evai G., Znojil M. (2000). Systematic search for PT symmetric potentials with real energy spectra. J. Phys. A: Math. Gen. 33 , 7165–7180.
  • [5] Feynmann R. and Hibbs A. (2010). Quantum Mechanics and Path Integrals. Emended Edition, Dover Publications Inc. Mineola, New York, 371s.
  • [6] Arai A. 1991). Exactly solvable supersymmetric quantum mechanics. J. Math. Anal Appl., 158, 63-79.
  • [7] Duru I.H., and Kleinert H.(1979). Solution of the path integral for the H-atom. Phys. Lett. B84, 185.
  • [8] Duru I.H. (1983). Morse-potential Green's function with path integrals. Phys. Rev. D, 28, 2689.
  • [9] Grosche C. (2005). Path integral solutions for deformed Poschl-Teller-like and conditionally solvable potentials. J. Phys. A: Math. Gen., 38, 2947-2958.
  • [10] Grosche C. (1989). Path integral solution of a class of potentials related to the Pöschl-Teller potential,. J. Phys. A: Math. Gen., 22, 5073-5087.
  • [11] Kandirmaz N. (2017). PT-/non-PT-Symmetric and Non-Hermitian Generalized Woods-Saxon Potential: Feynman Path Integral Approach GU j Sci.30(1), 133-138.
  • [12] Yesiltas O. (2007). PT/Non-PT Symmetric and Non-Hermitian Poschl-Teller-Like Solvable Potentials via Nikiforov-Uvarov Method. Phys. Scr., 75, 41-46.
  • [13]Alvarez-Castillo D.E. and Kirchbach M. (2007). Exact spectrum and wave functions of the hyperbolic Scarf potential in terms of finite Romanovski polynomials. Revista Mexicana de Fisica, E53(2), 143-154.
  • [14] Falaye, B. J. and Oyewumi, K. J. (2011). Solutions of the Dirac Equation with Spin and Pseudospin Symmetry for the Trigonometric Scarf Potential in D-dimensions. AfricanReview of Physics 6 (0025), 211–220.
  • [15] Suparmi A., Cari C., Deta UA. et al. (2014). Exact Solution of Dirac Equation for q-Deformed Trigonometric Scarf potential with q-Deformed Trigonometric Tensor Coupling Potential for Spin and Pseudospin Symmetries Using Romanovski Polynomial. Journal of Phys. Conference Series,539(2014), 012004.
  • [16] Arda A., Sever R. (2010). Effective-mass Klein–Gordon equation for non-PT/non-Hermitian generalized Morse potential. Phys.Scr., 82(6), 065007.
  • [17] Kandirmaz N., Sever R. (2009). Path Integral Solutions of PT-/Non-PT-Symmetric and Non-Hermitian Morse Potentials. Chinese J. Phys. 47,47.
  • [18] Kandirmaz N., Sever R. (2011). Path Integral Solution of PT-/non-PT-Symmetric and non-HermitianHulthen Potential, Acta Polytechnica, 51, 1.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Araştırma Makaleleri
Yazarlar

Nalan Kandırmaz 0000-0001-8212-1866

Yayımlanma Tarihi 30 Haziran 2020
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

APA Kandırmaz, N. (2020). Path Integral Yöntemiyle PT Simetrik/ PT Simetrik Hermityen Olmayan q-deformasyonlu Trigonometrik Scarf Potansiyeli. International Journal of Advances in Engineering and Pure Sciences, 32(2), 180-184. https://doi.org/10.7240/jeps.601583
AMA Kandırmaz N. Path Integral Yöntemiyle PT Simetrik/ PT Simetrik Hermityen Olmayan q-deformasyonlu Trigonometrik Scarf Potansiyeli. JEPS. Haziran 2020;32(2):180-184. doi:10.7240/jeps.601583
Chicago Kandırmaz, Nalan. “Path Integral Yöntemiyle PT Simetrik/ PT Simetrik Hermityen Olmayan Q-Deformasyonlu Trigonometrik Scarf Potansiyeli”. International Journal of Advances in Engineering and Pure Sciences 32, sy. 2 (Haziran 2020): 180-84. https://doi.org/10.7240/jeps.601583.
EndNote Kandırmaz N (01 Haziran 2020) Path Integral Yöntemiyle PT Simetrik/ PT Simetrik Hermityen Olmayan q-deformasyonlu Trigonometrik Scarf Potansiyeli. International Journal of Advances in Engineering and Pure Sciences 32 2 180–184.
IEEE N. Kandırmaz, “Path Integral Yöntemiyle PT Simetrik/ PT Simetrik Hermityen Olmayan q-deformasyonlu Trigonometrik Scarf Potansiyeli”, JEPS, c. 32, sy. 2, ss. 180–184, 2020, doi: 10.7240/jeps.601583.
ISNAD Kandırmaz, Nalan. “Path Integral Yöntemiyle PT Simetrik/ PT Simetrik Hermityen Olmayan Q-Deformasyonlu Trigonometrik Scarf Potansiyeli”. International Journal of Advances in Engineering and Pure Sciences 32/2 (Haziran 2020), 180-184. https://doi.org/10.7240/jeps.601583.
JAMA Kandırmaz N. Path Integral Yöntemiyle PT Simetrik/ PT Simetrik Hermityen Olmayan q-deformasyonlu Trigonometrik Scarf Potansiyeli. JEPS. 2020;32:180–184.
MLA Kandırmaz, Nalan. “Path Integral Yöntemiyle PT Simetrik/ PT Simetrik Hermityen Olmayan Q-Deformasyonlu Trigonometrik Scarf Potansiyeli”. International Journal of Advances in Engineering and Pure Sciences, c. 32, sy. 2, 2020, ss. 180-4, doi:10.7240/jeps.601583.
Vancouver Kandırmaz N. Path Integral Yöntemiyle PT Simetrik/ PT Simetrik Hermityen Olmayan q-deformasyonlu Trigonometrik Scarf Potansiyeli. JEPS. 2020;32(2):180-4.