J-matrix method of scattering in one dimension: The relativistic theory

• URL: http://arxiv.org/abs/2001.06298v1
• Date: Tue, 14 Jan 2020 19:02:15 GMT
• Title: J-matrix method of scattering in one dimension: The relativistic theory
• Authors: A. D. Alhaidari
• Abstract summary: We make a relativistic extension of the one-dimensional J-matrix method of scattering. The relativistic potential matrix is a combination of vector, scalar, and pseudo-scalar components.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We make a relativistic extension of the one-dimensional J-matrix method of scattering. The relativistic potential matrix is a combination of vector, scalar, and pseudo-scalar components. These are non-singular short-range potential functions (not necessarily analytic) such that they are well represented by their matrix elements in a finite subset of a square integrable basis set that supports a tridiagonal symmetric matrix representation for the free Dirac operator. Transmission and reflection coefficients are calculated for different potential coupling modes. This is the first of a two-paper sequence where we develop the theory in this part then follow it with applications in the second.

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