Physique Theorique et Mathematique
Institut de Physique, Bat B5,
Universite de Liege au Sart Tilman,
B-4000 Liege (Belgique)

e-mail: Jules.Beckers@ulg.ac.be

On the Heisenberg-Lie algebra and some non-hermitian operators in oscillatorlike developments

Abstract:
After a few generalities we compare fundamental quantum mechanics applied to the harmonic oscillator with unusual oscillatorlike developments dealing with non-hermitian operators, the latter aspect exploiting in particular the "relatively new" property of subnormality. In this last context we can also restore the hermiticity of the Hamiltonian operator discovering that its new nice property refers then to an interesting new scalar product. General constructions of oscillatorlike Hamiltonians are also considered and relatively "crazy" ideas in connection with the famous Heisenberg relations are presented.