- #1

George Keeling

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- Homework Statement
- This refers to problems A.28/29 from Quantum Mechanics – by Griffiths & Schroeter.

I am confused by the request for unitary diagonalising matrix.

- Relevant Equations
- T'=ST inverse(S), hermitian (U) = inverse (U)

This refers to problems A.28/29 from Quantum Mechanics – by Griffiths & Schroeter.

I’ve now almost finished the Appendix of this book and been greatly helped with the problems by Wolfram Alpha.

In problems A.28/29 we are asked to "Construct the unitary matrix S that diagonalizes T" where T is some matrix. The diagonal matrix is given by

$$\rm{}T^\prime=STS^{-1}$$The columns of ##\rm{}S^{-1}## are the eigenvectors of ##\rm{}T##. ##\rm{}S## diagonalises ##\rm{}T##.

A unitary matrix is one where the hermitian is the same as the inverse: ##\rm{}U^\dagger=U^{-1}##.

In neither question did ##\rm{}S^{-1}=S^\dagger##. So why are they asking for a "unitary matrix S"? Am I supposed to somehow manipulate ##\rm{}S## so it not only diagonalises ##\rm{}T## but is also unitary?

I’ve now almost finished the Appendix of this book and been greatly helped with the problems by Wolfram Alpha.

In problems A.28/29 we are asked to "Construct the unitary matrix S that diagonalizes T" where T is some matrix. The diagonal matrix is given by

$$\rm{}T^\prime=STS^{-1}$$The columns of ##\rm{}S^{-1}## are the eigenvectors of ##\rm{}T##. ##\rm{}S## diagonalises ##\rm{}T##.

A unitary matrix is one where the hermitian is the same as the inverse: ##\rm{}U^\dagger=U^{-1}##.

In neither question did ##\rm{}S^{-1}=S^\dagger##. So why are they asking for a "unitary matrix S"? Am I supposed to somehow manipulate ##\rm{}S## so it not only diagonalises ##\rm{}T## but is also unitary?