2000/12/31 by Evaldo M. F. Curado, E. M. F. Curado, M. A. Rego-Monteiro +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Class (philosophy) #Computer science #Creation and annihilation operators #Differential calculus #Geometry #Harmonic oscillator #Mathematics #Noncommutative geometry #Physics #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Square (algebra) #Type (biology) #hep-th
paper · pdf · doi:10.1103/physreva.64.012105
11 pages. The title and abstract were modified and minor corrections were made in the paper's core. Final version to appear in Phys. Rev. A
arxiv created 2001/05/14 · openalex publication_date 2001/06/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We construct a Heisenberg-like algebra for the one-dimensional infinite square-well potential in quantum mechanics. The ladder operators are realized in terms of physical operators of the system as in the harmonic-oscillator algebra. These physical operators are obtained with the help of variables used in a recently developed noncommutative differential calculus. This ``square-well algebra'' is an example of an algebra in a large class of generalized Heisenberg algebras recently constructed. This class of algebras also contains q oscillators as a particular case. We also discuss the physical content of this large class of algebras.