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math-ph2025
New quasi-exactly solvable systems from SUSYQM and Bethe Ansatz
Siyu Li, Ian Marquette, Yao-Zhong Zhang
We give a systematic construction of new quasi-exactly solvable systems via Bethe ansatz and supersymmetric quantum mechanics (SUSYQM). Methods based on the intertwining of superch…
math-ph2025
Polynomial deformations of and unified algebraic framework for solutions of a class of spin models
Siyu Li, Ian Marquette, Yao-Zhong Zhang
We introduce novel polynomial deformations of the Lie algebra . We construct their finite-dimensional irreducible representations and the corresponding differential operator…
math-ph2025
Stäckel transform, coupling constant metamorphosis and algebraization of quasi-exactly solvable systems
Siyu Li, Ian Marquette, Yao-Zhong Zhang
We generalize the notions of the Stäckel transform and the coupling constant metamorphosis to quasi-exactly solvable systems. We discover that for a variety of one-dimensional and…