量子库尔问题中的坐标空间修改：Fock理论调和张量
摘要
我们考虑Fock的 fundamental theory of the hydrogen atom in momentum space which allows a realization of the previously predicted rotation group of a three-dimensional (3D) sphere in four-dimensional (4D) space. 我们 then modify Fock's theory and abandon the momentum space description. 为了 transform and simplify the theory, we use invariant tensor methods of electrostatics in 3D and 4D spaces. 我们 find a coordinate 4D space where the Schrodinger equation becomes the 4D Laplace equation. 从 harmonic 4D polynomials to original 3D physical space 的转换是代数性的,并涉及对解释为 time 坐标的导数. 我们 obtain a differential equation for eigenfunctions in the momentum space and find its solutions. A concise calculation of the quadratic Stark effect is given. The Schwinger resolvent is derived by the method of harmonic polynomials. Vector ladder operators are also considered.
引用
@article{arxiv.2501.00010,
title = {Coordinate Space Modification of Fock's Theory-Harmonic Tensors in the Quantum Coulomb Problem},
author = {Sergei P. Efimov},
journal= {arXiv preprint arXiv:2501.00010},
year = {2025}
}
备注
38 pages, 1 figure