Selfadjoint extensions of operators and the teaching of quantum mechanics
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 selfadjoint operator. We then describe the selfadjoint 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 selfadjoint extensions of the Hamiltonian.
 Publication:

American Journal of Physics
 Pub Date:
 March 2001
 DOI:
 10.1119/1.1328351
 arXiv:
 arXiv:quantph/0103153
 Bibcode:
 2001AmJPh..69..322B
 Keywords:

 01.50.i;
 Educational aids;
 Quantum Physics;
 High Energy Physics  Theory
 EPrint:
 25 pages, Latex file, extended version of Am. J. Phys. 69 (2001) 322