I'm starting a series on "Quantum Mechanics Basics". Feel free to comment with any questions about the posted material. Be sure to stay tuned and enjoy!pic.twitter.com/NHmeD3kR4H
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are you assuming each eigenvalue has multiplicity one? How do you choose one eigenvector |a> in the eigenspace of the eigenvalue a?
no the eigenvalues are allowed to be degenerate, in which case an orthonormal basis can still be found by Graham Schmidt Orthogonalization and eigenvector is usually not chosen in QM, rather the representation of the operator O, and the eigenstates are the EVs
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ehm, I don't understand. We seem to have used different languages learning linear algebra (spoiler: we did
). What is |a>? Is it a specific, chosen eigejvector, or any eigenvector? -
oh it's just an arbitrary eigenvector of the operator A
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