N-dimensional Coulomb-Sturmians with noninteger quantum numbers

• URL: http://arxiv.org/abs/2602.01704v1
• Date: Mon, 02 Feb 2026 06:20:14 GMT
• Title: N-dimensional Coulomb-Sturmians with noninteger quantum numbers
• Authors: Ali Bagci,
• Abstract summary: Coulomb-Sturmian functions are complete, orthonormal, and include the full spectrum of continuum states.<n>Bagci-Hoggan exponential-type orbitals remove this restriction through a generalization to quantum number with fractional order.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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