Elektronik ve Haberleşme Mühendisliği Bölümü

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Diffraction in Time in the Relativistic Domain
(Elsevier Gmbh, 2021) Umul, Yusuf Ziya
The 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.
Citation - WoS: 2
Citation - Scopus: 3
Diffraction in Time of an Entangled Non-Relativistic Quantum Particle
(Iop Publishing Ltd, 2021) Umul, Yusuf Ziya
The diffraction process of an entangled non-relativistic quantum particle in time domain is investigated. The scenario consists of two entangled spin-0 particles and a quantum shutter, which is opened at an initial time. The particles are traveling in two opposite sides and expressed with a single wave function. The integral solution of the Schrodinger equation is considered for two particles case. The initial condition is expressed in terms of an entangled wave function. The time-diffracted matter wave is obtained in terms of the Fresnel integral. The effect of the phenomenon of diffraction in time is examined numerically for the entangled system of two particles.
Citation - WoS: 8
Citation - Scopus: 8
Kinetic Energy Based Relativistic Wave Equation
(Elsevier Gmbh, Urban & Fischer verlag, 2018) Umul, Yusuf Ziya
The Schrodinger equation is based on a Hamiltonian, which is the sum of kinetic and potential energies. The energy term, in the relativistic energy-momentum relation, is divided into its kinetic and rest energy components according to the Hamiltonian of the Schrodinger equation. The differential equation is obtained by using the plane wave representation. It is found that the derived form of the Klein-Gordon equation is more similar to the Schrodinger equation than the classical one. Non-relativistic limit is also studied.

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