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Physica E Low-dimensional Systems and Nanostructures

Exact quantum-mechanical solution for the one-dimensional harmonic oscillator model asymmetrically confined into the infinite well

E. I. Jafarov

Published Feb 8, 2022• 8 citations
Publisher
DOI
10.1016/j.physe.2022.115160

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In quantum mechanics with minimal length uncertainty relations the Heisenberg-Weyl algebra of the one-dimensional harmonic oscillator is a deformed SU(1,1) algebra. The eigenvalues and eigenstates are constructed algebraically and they form the infinite-dimensional representation of the deformed SU(1,1) algebra. Our construction is independent of prior knowledge of the exact solution of the Schrödinger equation of the model. The approach can be generalized to the DDD-dimensional oscillator with non-commuting coordinates.