New Mathematical Methods for Constructing Basis Sets in Multiple Coordinate Systems
Researchers have developed new techniques for constructing basis sets and Coulomb resolutions using generalized Laplacian symmetry operators across several separable coordinate systems, including two R-separable systems. The work expands the range of geometric configurations available for basis set construction, which has applications in both galactic dynamics and computational chemistry. This advancement is significant because it provides closed-form solutions using Jacobi polynomials and enables transformations between different coordinate systems, potentially improving computational efficiency in these fields.
A new mathematical framework has been developed for constructing basis sets in multiple separable coordinate systems using generalized Laplacian symmetry operators. The research derives three new basis sets—two in prolate spheroidal coordinates and one in cylindrical coordinates—all expressible in closed form using a single Jacobi polynomial. Additionally, the authors demonstrate how existing spherical polar or prolate spheroidal basis sets can be transformed into bispherical or toroidal basis sets. This work addresses a fundamental problem relevant to both galactic dynamics and computational chemistry by expanding the possible geometries in which basis set construction is feasible. The findings have been accepted for publication in the Journal of Physics A: Mathematical and Theoretical.
What different sources said
- arXiv astro-phCenter
Basis sets and Coulomb resolutions in rotational coordinates
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