Heisenberg-type structures of one-dimensional quantum Hamiltonians - art. no. 012105

We construct a Heisenberg-like algebra for the one-dimensional infinite squ are-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 u sed in a recently developed noncommutative differential calculus. This "squ are-well algebra'' is an example of an algebra in a large class of generali zed Heisenberg algebras recently constructed. This class of algebras also c ontains q oscillators as a particular case. We also discuss the physical co ntent of this large class of algebras.