Partial algebraization and a q-deformed harmonic oscillator
Abilio De Freitas, Sebastian Salamo
TL;DR
This paper develops an algebraic approach to solve the q-deformed 3D harmonic oscillator Schrödinger equation, providing exact solutions through a q-deformed su(2) algebra framework.
Contribution
It introduces a novel algebraic method for solving the q-deformed harmonic oscillator, extending quasi-solvable system techniques to q-deformed algebras.
Findings
Exact solutions for the q-deformed Schrödinger equation obtained.
Demonstrates the applicability of algebraic methods to q-deformed quantum systems.
Provides a foundation for further exploration of q-deformed quantum models.
Abstract
From the algebraic treatment of the quasi-solvable systems, and a q-deformation of the associated algebra, we obtain exact solutions for the q-deformed Schrodinger equation with a 3-dimensional q-deformed harmonic oscillator potential.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Nonlinear Waves and Solitons · Algebraic structures and combinatorial models