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GAZI UNIVERSITY JOURNAL OF SCIENCE

PT-/NON-PT-SYMMETRIC AND NON-HERMITIAN GENERALIZED WOODS-SAXON POTENTIAL: FEYNMAN PATH INTEGRAL APPROACH

Nalan Kandırmaz

Published Mar 14, 2017• 1 citation
OpenAlex

Abstract

In this paper, we examined the treatment path integral of the PT-/non-PT Symmetric and non-Hermitian Deformed Wood Saxon Potentials. Kernel, energy sperctrums and corresponding normalized wave functions of these potentials states are obtained. We used parametric time and point transformation for constructed kernel via path integral.

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Using the Nikiforov–Uvarov method which is based on solving the second-order differential equations, we firstly analyzed the energy spectra and eigenfunctions of the Woods–Saxon potential. In the framework of the PT-symmetric quantum mechanics, we secondly solved the time-independent Schrödinger equation for the PT and non-PT-symmetric version of the potential. It is shown that the discrete energy eigenvalues of the non-PT-symmetric potential consist of the real and imaginary parts, but the PT-symmetric one has a real spectrum. Results are obtained for s-states only.
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.
Using the Nikiforov-Uvarov method, the bound state energy eigenvalues and eigenfunctions of the PT-/non-PT-symmetric and non-Hermitian generalized Woods-Saxon (WS) potential with the real and complex-valued energy levels are obtained in terms of the Jacobi polynomials. According to the PT-symmetric quantum mechanics, we exactly solved the time-independent Schrodinger equation with same potential for the s-states and also for any l-state as well. It is shown that the results are in good agreement with the ones obtained before.