Self-adjoint extensions of operators and the teaching of quantum mechanics (original) (raw)
ADS
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Abstract
For the example of the infinite 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 settings. Additional physical requirements such as parity, time reversal, and positivity are used to restrict the large class of self-adjoint extensions of the Hamiltonian.
Publication:
American Journal of Physics
Pub Date:
March 2001
DOI:
10.48550/arXiv.quant-ph/0103153
arXiv:
Bibcode:
Keywords:
- 01.50.-i;
- Educational aids;
- Quantum Physics;
- High Energy Physics - Theory
E-Print:
25 pages, Latex file, extended version of Am. J. Phys. 69 (2001) 322