Two-body Coulomb problem and g(2) algebra (once again about the Hydrogen atom)
نویسندگان
چکیده
Taking the Hydrogen atom as an example it is shown that if symmetry of a three-dimensional system O(2)⊕Z2, variables (r,ρ,φ) allow separation variable φ, and eigenfunctions define new family orthogonal polynomials in two variables, (r,ρ2). These are related to finite-dimensional representations algebra gl(2)⋉R3∈g(2) (discovered by S Lie around 1880 which went almost unnoticed), occurs hidden G2 rational integrable 3 bodies on line with 2- 3-body interactions (the Wolfes model). Namely, those occur intrinsically study Zeeman effect atom. It quasi-exactly-solvable generalized Coulomb problem polynomial (r,ρ2)-variables found.
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ژورنال
عنوان ژورنال: Physics Letters
سال: 2023
ISSN: ['1873-2429', '0375-9601']
DOI: https://doi.org/10.1016/j.physleta.2023.128738