Solution of the Dirac Equation for Pseudo-Hermitian Hamiltonian and Energy-levels Crossing

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BAKHSHI ZAHRA; Soleimani Fereshte; Khoshdooni Sare

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Journal Paper

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Journal: Iranian Journal of Applied Physics Year:2021 | Volume:11 | Issue:2 (25) Page(s): 15-31

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Title

Solution of the Dirac Equation for Pseudo-Hermitian Hamiltonian and Energy-levels Crossing

Author(s)

BAKHSHI ZAHRA | Soleimani Fereshte | Khoshdooni Sare | Issue Writer Certificate

Keywords

Dirac Equation

Schrö

dinger Equation

Imaginary Potential

Pseudo-Hermitian Hamiltonian

Abstract

In this paper, the relativistic Dirac Equation in one dimension is investigated for a particle in an external electromagnetic field, with the property of position-dependent effective mass approximation (PDEM), in the absence of vector potential. By removing the lower spinor component and combining the pair of equations, a Schrö; dinger-like equation is obtained for the upper spinor component. Using canonical transformations and introducing two first-order Hermitian and anti-Hermitian differential operators, a formalism for pseudohermitic Hamiltonians with parity-time reversal symmetry (PT) has been obtained. Comparing the equation derived from Pseudo-Hermitian Hamiltonian with the non-relativistic Schrö; dinger Equation leads to a general formalism for one-dimensional solvable imaginary non-Hermitian potentials with real energy spectra. Also, using this process, the complex potentials of Pö schl-Teller and Scarf II with real energy spectra in Dirac Equation with PDEM approximation and PT symmetry have been investigated and their application has been expressed. For some particular parameters we will see the phenomenon of energy-levels crossing. In fact, it means that energy levels disappear from the spectrum. Also, for the mentioned examples, potential figures are drawn.

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APA: Copy

BAKHSHI, ZAHRA, Soleimani, Fereshte, & Khoshdooni, Sare. (2021). Solution of the Dirac Equation for Pseudo-Hermitian Hamiltonian and Energy-levels Crossing. IRANIAN JOURNAL OF APPLIED PHYSICS, 11(2 (25) ), 15-31. SID. https://sid.ir/paper/411285/en

Vancouver: Copy

BAKHSHI ZAHRA, Soleimani Fereshte, Khoshdooni Sare. Solution of the Dirac Equation for Pseudo-Hermitian Hamiltonian and Energy-levels Crossing. IRANIAN JOURNAL OF APPLIED PHYSICS[Internet]. 2021;11(2 (25) ):15-31. Available from: https://sid.ir/paper/411285/en

IEEE: Copy

ZAHRA BAKHSHI, Fereshte Soleimani, and Sare Khoshdooni, “Solution of the Dirac Equation for Pseudo-Hermitian Hamiltonian and Energy-levels Crossing,” IRANIAN JOURNAL OF APPLIED PHYSICS, vol. 11, no. 2 (25) , pp. 15–31, 2021, [Online]. Available: https://sid.ir/paper/411285/en

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