Principles of Quantum Mechanics · Problem 1.8.7

Mathematical Introduction — R. Shankar

Physics — Quantum Mechanics · eigenvalues-trace-determinant

Problem

By using the results on the trace and determinant from the last problem, show that the eigenvalues of the matrix Ω=[1221]\Omega = \begin{bmatrix} 1 & 2 \\ 2 & 1 \end{bmatrix} are 3 and −1-1. Verify this by explicit computation. Note that the Hermitian nature of the matrix is an essential ingredient.

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