N-dimensional Coulomb-Sturmians with noninteger quantum numbers
Abstract
Coulomb-Sturmian functions are complete, orthonormal, and include the full spectrum of continuum states. They are restricted to integer values of quantum numbers, as imposed by boundary and orthonormality conditions. Bagci-Hoggan exponential-type orbitals remove this restriction through a generalization to quantum number with fractional order. The differential equations for N-dimensional Bagci-Hoggan orbitals are derived. It is demonstrated that Coulomb-Sturmian functions satisfy a particular case of these equations. Additionally, Guseinov's Psi-alpha-ETOs are identified as N-dimensional Coulomb-Sturmians with a shifted dimensional parameter alpha, rather than representing an independent complete orthonormal sets of basis in a weighted Hilbert space.
Keywords
Cite
@article{arxiv.2602.01704,
title = {N-dimensional Coulomb-Sturmians with noninteger quantum numbers},
author = {Ali Bagci},
journal= {arXiv preprint arXiv:2602.01704},
year = {2026}
}