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Topic 35: Properties of Correlation Matrices (PETARS, Chapter 5)
Topic 35: Properties of Correlation Matrices (PETARS, Chapter 5)
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A particular matrix is both Hermitian and unitary. Show that its eigenvalues are all ±1. Note. The Pauli and Dirac matrices are specific examples. | Numerade
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numerade.com
Starting with a momentum operator 𝐩 having eigenstates |𝐩^'⟩, define an infinitesimal boost operator ℬ(d 𝐩^') that changes one momentum eigenstate into another, that is ℬ(d 𝐩^')|𝐩^'⟩=|𝐩^' d 𝐩^'⟩. Show that the form ℬ(d 𝐩^')=1 i 𝐖 ·d 𝐩^', where 𝐖 is Hermitian, satisfies the unitary, associative, and inverse properties that are appropriate for ℬ(d 𝐩^'). Use dimensional analysis to express 𝐖 in terms of the position operator 𝐱, and show that the result satisfies the canonical commutat
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