Observables in Quantum Mechanics and the Importance of Self-adjointness

Abstract

We are focused on the idea that observables in quantum physics are a bit more than 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.

arXiv comment37 pages, new and improved version, various paragraphs added, accepted for publication

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• Passive quantum measurement: Arrival time, quantum Zeno effect and gambler's fallacy
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