Riley hobson bence · Problem 19.5

Quantum operators

Mathematics — Methods · quantum-operators-matrix-functions

Problem

For the matrix

\mathsf{C} = \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}

, evaluate

\cos \mathsf{C}

and

\sin \mathsf{C}

, and verify that

\cos \mathsf{C} = \cos\sqrt{2}\begin{pmatrix}1 & 0 \\ 0 & 1\end{pmatrix}, \quad \sin \mathsf{C} = \frac{\sin\sqrt{2}}{\sqrt{2}}\begin{pmatrix}1 & 1 \\ 1 & -1\end{pmatrix}.