Question

It's a quantum mechanics problem.

Consider the 2 x 2 matrix defined by
aoi a
U
.
(5)
ао — iд .a
where ao 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 matrix represents a rotation in three dimensions. Find the
axis and angle of rotation appropriate for U in terms of ao, ai, a2, a3

Image Transcription

Consider the 2 x 2 matrix defined by aoi a U . (5) ао — iд .a where ao 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 matrix represents a rotation in three dimensions. Find the axis and angle of rotation appropriate for U in terms of ao, ai, a2, a3

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