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On (p, q; α, β, l)-deformed oscillators and their oscillator algebras

I. M. Burban
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Abstract

We present a description of a new kind of the deformed canonical commutation relations, their representations and generated by them Heisenberg-Weyl algebra. This deformed algebra allows us to derive operations of the Hopf algebra structure: comultiplication, counit and antipode. We discuss properties of a discrete spectrum of the Hamiltonian of the deformed harmonic oscillator corresponding to this oscillator-like system.

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I. M. Burban. 2006-09-15. On (p, q; α, β, l)-deformed oscillators and their oscillator algebras. https://arxiv.org/abs/math/0609441

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