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American Journal of Physics

Operator domains and self-adjoint operators

Vanilse S. Araujo, Francisco Antônio Bezerra Coutinho, J. Fernando Perez

Published Jan 14, 2004• 78 citations
Publisher

Abstract

To construct a self-adjoint operator the domain of the operator has to be specified by imposing an appropriate boundary condition or conditions on the wave functions on which the operator acts. We illustrate situations for which different boundary conditions lead to different operators and hence to different physics.
DOI
10.1119/1.1624111

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We are focused on the idea that observables in quantum physics are a bit more then just hermitian operators and that this is, in general, a “tricky business”. The origin of this idea comes from the fact that there is a subtle difference between symmetric, hermitian, and self-adjoint operators which are of immense importance in formulating Quantum Mechanics. The theory of self-adjoint extensions is presented through several physical examples and some emphasis is given on the physical implications and applications.