PATH INTEGRAL SOLUTIONS OF PT-/NON-PT SYMMETRIC AND NON-HERMITIAN DENG-FAN MOLECULAR POTENTIAL

Year 2020, Volume: 8 Issue: 2, 182 - 190, 31.08.2020

Nalan Kandırmaz

https://doi.org/10.20290/estubtdb.601938

Abstract

Bu çalışmada PT-/PT Simetrik ve Hermityen olmayan Deng-Fan Moleküler potansiyelinin Path integral davranışı incelendi. Uygun koordinat ve momentum dönüşümleri ve parametrik zaman tanımlanarak sistemin kerneli elde edildi. Path integral yöntemi uygulanarak sistemin enerji özdeğerleri ve dalga fonksiyonlarını veren Green's fonksiyonu hesaplandı. PT-/PT Simetrik ve non hermityen olmayan sistemin enerji özdeğerleri ve karşılık gelen dalga fonksiyonları elde gösterildi.

In this study, Path integral behavior of Parity-Time (PT)-/non-PT- Symmetric and Non-Hermitian Deng-Fan Molecular potential is examined. Appropriate coordinate and momentum transformations and parametric time were defined and the kernel of the system was found. By applying the path integral method, Green's function, which gives energy eigenvalues and wave functions of the system, is evaluated. Energy eigenvalues and corresponding wave functions of PT- / PT Symmetric and Non-Hermitian systems were obtained.

Keywords

Path Integral, PT Symmetry, Non-Hermitian Potentials, Deng-Fan Molecular Potentials

PATH INTEGRAL SOLUTIONS OF PT-/NON-PT SYMMETRIC AND NON-HERMITIAN DENG-FAN MOLECULAR POTENTIAL

Abstract

In this study, Path integral behavior of Parity-Time (PT)-/non-PT- Symmetric and Non-Hermitian Deng-Fan Molecular potential is examined. Appropriate coordinate and momentum transformations and parametric time were defined and the kernel of the system was found. By applying the path integral method, Green's function, which gives energy eigenvalues and wave functions of the system, is evaluated. Energy eigenvalues and corresponding wave functions of PT- / PT Symmetric and Non-Hermitian systems were obtained.

Bu çalışmada PT-/PT Simetrik ve Hermityen olmayan Deng-Fan Moleküler potansiyelinin Path integral davranışı incelendi. Uygun koordinat ve momentum dönüşümleri ve parametrik zaman tanımlanarak sistemin kerneli elde edildi. Path integral yöntemi uygulanarak sistemin enerji özdeğerleri ve dalga fonksiyonlarını veren Green's fonksiyonu hesaplandı. PT-/PT Simetrik ve non hermityen olmayan sistemin enerji özdeğerleri ve karşılık gelen dalga fonksiyonları elde gösterildi.

Keywords

Path İntegrali, PT-Simetri, Hermityen olmayan Potansiyeller, Deng-Fan Molekül Potansiyeli

References

• [1] Landau, L. D, Lifshitz E.M. Mechanics, Third Edition, UK, Pergamon Press, 1976.
• [2] Feynman, R. P, Hibbs A.R. Quantum Mechanics and Path Integrals, Emended Addition, New York: Dover Publications Inc, Mineola, 2010.
• [3] Duru I.H and Kleinert H. Solution of the path integral for the H-atom. Phys. Lett. 1979; B84., 185.
• [4] Duru I. H. On The Path Integrations for the Wood-Saxon and Related Potentials. Phys. Lett. A 1986; 119(4).
• [5] Kandirmaz N. PT-/non-PT-Symmetric and Non-Hermitian Generalized Woods-Saxon Potential: Feynman Path Integral Approach. GU. J.Sci. (2017); 30(1), 133-138.
• [6] Kandirmaz N, Sever R. Path Integral Solutions of PT-/Non-PT-Symmetric and Non-Hermitian Morse Potentials Chinese J. Phys. 2009; 47, 47.
• [7] Kandirmaz N, Sever R. Path Integral Solution of PT-/Non-PT-Symmetric and Non-Hermitian Hulthen Potential, Acta Polytechnica 2011; 51,1.
• [8] Grosche C. Path integral solutions for deformed Pöschl-Teller like and conditionally solvable potentials J. Phys., A: Math. Gen. 2005; 38, 2947-2958.
• [9] Grosche C. Path integral solution of a class of potentials related to the Pösch-Teller potential. J. Phys. A: Math. Gen. 1989; 22, 5073-5087.
• [10] Bender C. M, Boettcher S. Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry,” Phys. Rev. Lett. 1998; 80, 5243.
• [11] Bender CM. PT-symmetric quantum theory. Journal of Physics: Conference Series 2011; 63, 012002.
• [12] Mostafazadeh A. Pseudo-Hermiticity versus PT-symmetry. II. A complete characterization of non-Hermitian Hamiltonians with a real spectrum. J. Math. Phys. 2002; 43, 2814.
• [13] Arda A, Sever R. PT-/non-PT-symmetric and non-Hermitian Hellmann potential: approximate bound and scattering states with any ℓ-values Phys. Scr. 2014; 89, 105204.
• [14] Hamzavi M, Ikhdair S.M. Equivalence of the empirical shifted Deng–Fan oscillator potential for diatomic molecules. J Math. Chem. 2013; 51, 227-238.
• [15] Rong, Z., Kjaergaard, H.G., Sage, M.L. Comparison of the Morse and Deng-Fan potentials to treating the X-H stretching motion in small molecules. Mol Phys . 2003; 101, 2285–2294.
• [16] Diaf A. Arbitrary ℓ-state solutions of the Feynman propagator with the Deng-Fan molecular potential Journal of Physics: Conference Series 2015; 574, 012022.
• [17] Dong SH, Gu XY. Arbitrary l state solutions of the Schrödinger equation with the Deng-Fan molecular potential. J.Phys. Conference Series 2008; 96, 012109.
• [18] Kleinert H.and Mustapic I. Summing the Spectral Representations of Pöschl-Teller and Rosen-Morse Fixed-Energy Amplitudes. J.Math. Phys. 1992; 33, 643-662.