Principles of Quantum Mechanics · Problem 1.6.6

Mathematical Introduction — R. Shankar

Physics — Quantum Mechanics · unitary-operators

Problem

Verify that the following matrices are unitary:

\frac{1}{2^{1/2}}\begin{bmatrix} 1 & i \\ i & 1 \end{bmatrix}, \qquad \frac{1}{2}\begin{bmatrix} 1+i & 1-i \\ 1-i & 1+i \end{bmatrix}

Verify that the determinant is of the form

e^{i\theta}

in each case. Are any of the above matrices Hermitian?