Talbot Effect with Matter Waves¹

Farhan Saif

Department of Electronics, Quaid-i-Azam University, Islamabad 45320, Pakistan

Center for Applied Mathematics and Physics, National University of Science and Technology, Islamabad, Pakistan

e-mail: farhan.saif@qau.edu.pk

Received April 25, 2012

Abstract—Talbot effect in the space-time evolution of matter waves is analyzed and shown that the matter
waves at relativistic and non-relativistic velocities exhibit coherence beyond the grating and display Talbot self-
imaging. The grating is realized by considering equidistant narrowly peaked coherent probability distributions
at the onset. Theoretical frame work is based on a quantum particle at relativistic and non-relativistic velocities
in a one dimensional box. The matter waves, in their evolution, display Talbot self-imaging and fractional self-
imaging as restructuring, respectively, at Talbot length and fractional Talbot lengths.

DOI: 10.1134/S1054660X12120079

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