Posgrado en Ciencias Físicas, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理科学研究生项目）；Instituto de Ciencias Físicas Universidad Nacional Autónoma de México（墨西哥国立自治大学物理科学学院）
Kenan Uriostegui, Kurt Bernardo Wolf
发表信息：
Applied Mathematics & Information Sciences 15, No. 3, 307-315 (2021)
The two-dimensional Helmholtz equation separates in elliptic coordinates based on two distinct foci, a limit case of which includes polar coordinate systems when the two foci coalesce. This equation is invariant under the Euclidean group of translations and orthogonal transformations; we replace the latter by the discrete dihedral group of N discrete rotations and reflections. The separation of variables in polar and elliptic coordinates is then used to define discrete Bessel and Mathieu functions, as approximants to the well-known continuous Bessel and Mathieu functions, as N-point Fourier transforms approximate the Fourier transform over the circle, with integrals replaced by finite sums. We find that these 'discrete' functions approximate the numerical values of their continuous counterparts very closely and preserve some key special function relations.
Posgrado en Ciencias Físicas, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理科学研究生院）；Instituto de Ciencias Físicas Universidad Nacional Autónoma de México（墨西哥国立自治大学物理科学学院）
Transparent boundary conditions for the spatially discrete Schrödinger equation: Reflectionless quantum transport in 1D lattices
National University of Uzbekistan（乌兹别克斯坦国立大学）；Kimyo International University in Tashkent（塔什干化学国际大学）；Bergische Universität Wuppertal（伍珀塔尔大学）；Turin Polytechnic University in Tashkent（塔什干都灵理工大学）
