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Solvable Potentials for the 1D Dirac Equation Using the Tridiagonal Matrix Representations

机译:使用Tridiagonal矩阵表示的1D DIRAC方程的可溶性电位

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The aim of this research is to extend the class of solvable potentials of Dirac equation as a continuation to the work in [1]. We expand the spinor wavefunction in a square integrable spinor basis functions in which the expansion coefficients are functions of energy and potential parameters. Requiring the wave operator, J = H - E, to be tridiagonal and symmetric, this transforms the wave equation to a three-term recursion relation for the expansion coefficients which can be solved using known mathematical results on orthogonal polynomials. For illustration, we restricted ourselves here to the so-called Laguerre basis and considered situations where the obtained recursion relations can be easily compared to the ones associated with a well-known class of orthogonal polynomials.
机译:本研究的目的是将DIRAC方程的可溶性电位类扩展为[1]的工作的延续。我们在方形可完善的旋锭基函数中扩展旋转轨道功能,其中膨胀系数是能量和潜在参数的功能。要求波算子J = H-E,以三角形和对称,这将波浪方程变换为扩展系数的三术递归关系,其可以在正交多项式上使用已知的数学结果来解决。为了插图,我们在这里限制了自己的所谓Laguerre基础,并考虑了与与着名的正交多项式相关联的递归关系可以轻松地进行所获得的递归关系的情况。

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