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Global Journal of Human Social Science

Path Integral Solutions of the PT-Symmetric and Non-Hermitian q-deformed Eckart Plus Modified Hylleraas Potential

Nalan Kandırmaz

Published Aug 22, 2018• 0 citations
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Abstract

In this study, the wave functions and the energy spectrum of the PT-Symmetric and non-Hermitian q-deformed Eckart plus modified Hylleraas potential are studied using Feyman's Path In-tegral method. The kernel and Green.s Function for PT-Symmetric and non-Hermitian qdeformed Eckart plus modified Hylleraas potential is analytically derived by transforming spacetime. The results are discussed for the different parameters of the potential.

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In this study, the wave functions and the energy spectrum of the PT-Symmetric and non-Hermitian q-deformed Eckart plus modified Hylleraas potential are studied using Feyman's Path In-tegral method. The kernel and Green.s Function for PT-Symmetric and non-Hermitian qdeformed Eckart plus modified Hylleraas potential is analytically derived by transforming spacetime. The results are discussed for the different parameters of the potential.
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.
We have obtained approximate bound state solutions of Schrödinger wave equation with modified quadratic Yukawa plus q-deformed Eckart potential Using Parametric Nikiforov-Uvarov (NU) method. However, we obtained numerical energy eigenvalues and un-normalized wave function using confluent hypergeometric function (Jacobi polynomial). With some modifications, our potential reduces to a well-known potential such as Poschl-Teller and exponential inversely quadratic potential. Numerical bound state energies were carried out using a well-designed Matlab algorithm while the plots were obtained using origin software. The result obtained is in agreement with that of the existing literature.