Introduction to Quantum Mechanics · Problem A.11

Afterword — David J. Griffiths

Physics — Quantum Mechanics · matrices

Problem

Prove Equations A.52, A.53, and A.58: (ST~)=T~S~,(ST)†=T†S†,(ST)−1=T−1S−1.(\widetilde{\mathsf{ST}}) = \tilde{\mathsf{T}}\tilde{\mathsf{S}}, \quad (\mathsf{ST})^\dagger = \mathsf{T}^\dagger \mathsf{S}^\dagger, \quad (\mathsf{ST})^{-1} = \mathsf{T}^{-1}\mathsf{S}^{-1}. Show that the product of two unitary matrices is unitary. Under what conditions is the product of two hermitian matrices hermitian? Is the sum of two unitary matrices necessarily unitary? Is the sum of two hermitian matrices always hermitian?

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