Consider the 2 x 2 matrix defined by where a 0 is a real number and a

Question:

Consider the 2 x 2 matrix defined by

where a₀ is a real number and a is a three dimensional vector with real components.

(a) Prove that U is unitary and unimodular.

(b) In general, a 2 x 2 unitary unimodular matri x represents a rotation in three dimensions. Find the axis and angle of rotation appropriate for U in terms of a₀ , a₁, a₂, and a₃.

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Modern Quantum Mechanics

ISBN: 9780805382914

2nd Edition

Authors: J. J. Sakurai, Jim J. Napolitano

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Question Posted: Aug 05, 2023 07:45 AM

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Consider the 2 x 2 matrix defined by where a 0 is a real number and a

Question:

U= = ao + io.a ao-io a

Step by Step Answer:

a To prove that a 2x2 matrix U is unitary we need to show that its conjugate transpose U is equal to ...View the full answer

Modern Quantum Mechanics

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