Vestnik КRAUNC. Fiz.-Mat. Nauki. 2026. vol. 54. no. 1. P. 141 – 153. ISSN 2079-6641

PHYSICS
https://doi.org/10.26117/2079-6641-2026-54-1-141-153
Research Article
Full text in English
MSC 81Q60, 81Q80, 81V45

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Non-Hermitian Supersymmetric Factorization of an Effective Two-Particle Hamiltonian in Two Dimensions under a Magnetic Field

J. A. Oke¹², F. A. Dossa¹²³^{\ast}

¹National University of Science, Technology, Engineering and Mathematics (ED-STIM), Goho, Abomey, Republic of Benin
²Laboratory of Physics and Applications (LPA), University Center of Natitingou, National University of Science, Technology, Engineering and Mathematics (UNSTIM), Quartier Bagri, Natitingou, Republic of Benin
³National University of Science, Technology, Engineering and Mathematics (UNSTIM), Quartier Bagri, Natitingou, Republic of Benin

Abstract. We study an effective Hamiltonian governing the relative motion of two charged particles confined to a two-dimensional plane under a uniform magnetic field, with interactions described by a generalized central potential that combines harmonic, Coulombic, linear, and inverse-square terms. After formal separation of the center-of-mass coordinates and a unitary transformation to a standard one-dimensional radial Hilbert space, the resulting equation is solved exactly through a non-Hermitian supersymmetric factorization: although the factorization operators are not mutually adjoint, they yield Hermitian partner Hamiltonians that exhibit shape invariance with respect to a weighted inner product, enabling the derivation of closed-form analytical expressions for the energy spectrum and radial wave functions. The constraint relation among potential parameters that emerges from this construction is not a physical law but a mathematical solvability condition–an essential feature of a deliberately idealized model whose purpose is to reveal novel algebraic structures underlying exactly solvable quantum systems. We explicitly discuss the formal nature of the model, the parameter regimes ensuring potential boundedness, and the mathematical framework required for self-adjointness.

Key words: Hamiltonian, magnetic field, non-Hermitian factorization.

Received: 24.12.2025; Revised: 24.02.2026; Accepted: 03.03.2026; First online: 29.03.2026

For citation. Oke J. A., Dossa F. A. Non-Hermitian supersymmetric factorization of an effective two-particle Hamiltonian in two dimensions under a magnetic field. Vestnik KRAUNC. Fiz.-mat. nauki. 2026, 54: 1, 141-153. EDN: TTTUMU. https://doi.org/10.26117/2079-6641-2026-54-1-141-153.

Funding. Not funding

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

^{\ast}Correspondence: E-mail: dossafanselme@gmail.com
The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Oke J. A., Dossa F. A., 2026

© Institute of Cosmophysical Research and Radio Wave Propagation, 2026 (original layout, design, compilation)

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