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

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

2001-03-28

arxiv.org/abs/quant-ph/0103153v1

Am.J.Phys. 69 (2001) 322

Physics

Quantum Physics

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

Scientific paper

10.1119/1.1328351

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.

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