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.

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

References in corpus (7)

• Kappa-Minkowski space-time and the star product realizations
• Dirac Hamiltonian with superstrong Coulomb field
• Electron Capture and Scaling Anomaly in Polar Molecules
• Canonical quantization on the half-line and in an interval based upon a new concept for the momentum in a space with boundaries
• Self-adjoint Schrodinger and Dirac operators with Aharonov-Bohm and magnetic-solenoid fields
• "Quantization is a mystery"
• Entropy non-conservation and boundary conditions for Hamiltonian dynamical systems

Cited by in corpus (7)

• Anomalous Bootstrap on the half line
• Bouncing Wave Packets, Ehrenfest Theorem, and Uncertainty Relation based upon a new Concept for the Momentum of a Particle in a Box
• Role of anomalous symmetry in 0-$\pi$ qubits
• Bound states without potentials: localization at singularities
• Passive quantum measurement: Arrival time, quantum Zeno effect and gambler's fallacy
• Bootstrapping periodic quantum systems
• All Hilbert spaces are the same: consequences for generalized coordinates and momenta