A spin observable is represented by the Hermitian matrix

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Quantum Mechanics · Linear algebra and vector spaces

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Spin one-half, the Pauli matrices and two-level systems

Problem

M = \dfrac{\hbar}{2}\begin{pmatrix}0.6&0.8\\ 0.8&-0.6\end{pmatrix}

. Using the method of this chapter's worked example, find its eigenvalues and normalised eigenvectors, and check the eigenvectors are orthogonal.