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

Abstract

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.

25 pages, Latex file, extended version of Am. J. Phys. 69 (2001) 322

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