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 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.