Elektronik ve Haberleşme Mühendisliği Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/260
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Article Diffraction in Time in the Relativistic Domain(Elsevier Gmbh, 2021) Umul, Yusuf ZiyaThe diffraction of matter waves in time is investigated by using the kinetic energy based relativistic wave equation for the quantum shutter problem. The differential equation is solved with the aid of the Fourier integral transform according to the spatial coordinate. A new Green's function is obtained and a scattering integral is composed for the wave function. The boundary condition of the quantum shutter problem is expressed in the kernel of the integral. Two field components are derived by the asymptotic evaluation of the scattering integral. The behavior of the scattered matter waves is studied in the relativistic and non-relativistic domains numerically.Article Citation - WoS: 2Citation - Scopus: 2Airy-Type Relativistic Matter Wave(Elsevier Gmbh, 2021) Umul, Yusuf ZiyaA new relativistic Airy-type matter wave is introduced as a solution of the kinetic energy based wave equation. The parametric solution of the related differential equation is obtained. The total energy and momentum of the relativistic particle are derived by using a Bohmian type of decomposition of the kinetic energy based equation. The acceleration of the particle is also evaluated. The behavior of the matter wave is investigated numerically.Article Citation - Scopus: 1Relativistic Wave Equation for a Quantum Particle With Potential Energy(Elsevier Gmbh, 2019) Umul, Yusuf ZiyaA new relativistic wave equation is derived for a quantum particle which moves in a potential. The relativistic equation of energy is reconsidered with the potential energy term. The energy-momentum relation is obtained for this case. The related differential equation is derived by taking into account a wave function in terms of a plane wave. It is shown that the new equation directly reduces to the Schrodinger equation of a particle, moving in a potential in the non-relativistic limit. The wave equation is applied to the interaction of wave function with a potential barrier.Article A New Approach To the Dirac Equation(Elsevier Gmbh, 2019) Umul, Yusuf ZiyaDirac equation is based on a novel method that expresses the roots of a square-root operation in terms of matrices. Instead of this technique we propose an alternative approach. The square-root expression is represented as a hypotenuse and it is written in terms of a trigonometric summation of the remaining two edges of a right-angle triangle. Both of the positive and negative energy terms are taken into account and a new matrix equation is obtained. The plane wave solutions of the new differential equation are studied.Article Citation - WoS: 1Citation - Scopus: 1Kinetic Energy Based Relativistic First Order Wave Equations(Elsevier Gmbh, 2019) Umul, Yusuf ZiyaA relativistic wave equation is derived for spin-1/2 particles. The energy relation is taken into account with respect to the kinetic energy term. Two first order differential equations are obtained from the kinetic energy based relativistic equations. The spin information is integrated to the new equations in two alternative forms.