J-matrix method of scattering in one dimension: The nonrelativistic theory - Mathematical PhysicsReport as inadecuate




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Abstract: We formulate a theory of nonrelativistic scattering in one dimension based onthe J-matrix method. The scattering potential is assumed to have a finite rangesuch that it is well represented by its matrix elements in a finite subset of abasis that supports a tridiagonal matrix representation for the reference waveoperator. Contrary to our expectation, the 1D formulation reveals a rich andhighly non-trivial structure compared to the 3D formulation. Examples are givento demonstrate the utility and accuracy of the method. It is hoped that thisformulation constitutes a viable alternative to the classical treatment of 1Dscattering problem and that it will help unveil new and interestingapplications.



Author: A. D. Alhaidari, H. Bahlouli, M. S. Abdelmonem

Source: https://arxiv.org/







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