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The European Physical Journal Plus

Energy-dependent one-dimensional potentials and scattering of relativistic particles

H. Tilaver, Hilmi Yanar, Mustafa Saltı, Oktay Aydogdu A

Published Jan 26, 2021• 3 citations
Publisher
DOI
10.1140/epjp/s13360-021-01135-2

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Non-relativistic Fermi particle in one-dimensional pseudoscalar δδδ-function potential
It is shown that a non-relativistic Fermi particle with a non-zero rest energy moving in a pseudoscalar δδδ-function potential in one dimension can be confined for both signs of the coupling constant. The binding energies depend on the value of the particle's rest energy, and in the limit of vanishing rest energy only one of the bound states survives. The coefficients of reflection and transmission are determined, and the conditions for complete reflection and transmission are discussed.
Abstract This study aims to address the nature of state change, measurement, and probabilistic outcomes in non-relativistic quantum mechanics. We consider a pair of particles that interact in a one-dimensional setting via a delta-function potential. One of the particles is confined to a one-dimensional box, and the other particle is free. The free particle is incident from the left with specified energy, and it may cause changes in state of the confined particle before flying away to the left or to the right. We present a formulation and computational scheme that avoids the use of perturbation theory and determines the probability of any such outcome as a function of the initial state of the confined particle and the energy of the incident particle. As demonstrated by a direct comparison, this presented method holds multiple advantages over a standard perturbative method. The problem formulation and corresponding computational scheme may have applications in physical settings which admit one-dimensional scattering, e.g., in the study of quantum wires or quantum dots.