Introduction to Quantum Mechanics · Problem A.23

Afterword — David J. Griffiths

Physics — Quantum Mechanics · changing-bases

Problem

Show that if two matrices commute in one basis, then they commute in any basis. That is: [T1e,T2e]=0⇒[T1f,T2f]=0.\left[\mathsf{T}_1^e, \mathsf{T}_2^e\right] = 0 \Rightarrow \left[\mathsf{T}_1^f, \mathsf{T}_2^f\right] = 0. Hint: Use Equation A.64.

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