Diffraction in time in the relativistic domain

Abstract

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.