Abstract
We are focused on the idea that observables in quantum physics are a bit more then 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.
Highlights
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We can ask ourselves a natural question: “What are the possible choices of boundary conditions for a given operator representing an observable in Quantum Mechanics (QM)?”. Before we address this question we must remember that observables in QM must have real eigenvalues
Concluding that H is SA in Dα ( H ). This shows that by enlarging the domain of H has reduced the domain of H † in such a way that they are equal and the operator is SA
Summary
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