PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Quantum Mechanics · The formalism of quantum mechanics
The Structure of Quantum Mechanics, Ch Observables, spectra and the spectral theorem
Problem
A spin-half operator is A^=∣↑⟩⟨↓∣+2i∣↓⟩⟨↑∣.
((a)) Write the matrix Amn=⟨m∣A^∣n⟩ in the basis {∣↑⟩,∣↓⟩}.
((b)) Use (A^†)mn=Anm∗ to write the matrix of A^†.
((c)) Decide whether A^ is Hermitian, and whether it is unitary.