ABSTRACT: In this work we present the solution of the Dirac equation with sine and cosine functions as extensions. In both cases, we find the same probability distribution which is a continuous spatial function with locally bound states. It is also observed that the particle has periodic momentum. It is expected from this work that the equation will have applications in condensed matter physics and nanophysics
Keywords: Modified Dirac equation, Space dependent probability, periodic momentum, Gaussian probability
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