Observables, Operators, Eigenvectors, and Eigenvalues I

In this chapter, we will discuss observables. Observables are related to the physical quantities that can be measured and observed. The measured/observed values are the eigenvalues of the corresponding operators. Therefore, the corresponding operators of the observables must have real eigenvalues. We will use Pauli spin matrices that correspond to spin measurements as examples. We will practice how to find the eigenvalues and eigenvectors of the Pauli matrices. Finally, we will briefly discuss the eigenspace of degenerated eigenvectors.