Self-adjoint extensions of operators and the teaching of quantum mechanics

Guy Bonneau, Jacques Faraut, Galliano Valent

Published 2001-03-28Version 1

For the example of the infinitely deep well potential, we point out some paradoxes which are solved by a careful analysis of what is a truly self-adjoint operator. We then describe the self-adjoint extensions and their spectra for the momentum and the Hamiltonian operators in different physical situations. Some consequences are worked out, which could lead to experimental checks.