Heisenberg-type structures of one-dimensional quantum Hamiltonians

Abstract

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 non commutative differential calculus. This \textquotedblleft square-well algebra\textquotedblright 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.

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

Cited by in corpus (8)

• Construction of coherent states for physical algebraic systems
• Generalized Heisenberg Algebras and Fibonacci Series
• Generalized quantum field theory: perturbative computation and perspectives
• A Method Based on a Nonlinear Generalized Heisenberg Algebra to Study the Molecular Vibrational Spectrum
• Non-linear generalization of the sl(2) algebra
• Construction of a non-standard quantum field theory through a generalized Heisenberg algebra
• Some boundary effects in quantum field theory
• Lattice oscillator model on noncommutative space: eigenvalues problem for the perturbation theory