Last Updated：2022/12/23
Sentence
The
eigenvectors
of
the
first
Pauli
matrix
"encode"
—
as
it
were
—
the
+X
and
−X
directions.
Likewise,
the
eigenvectors
of
the
second
Pauli
matrix
"encode"
the
+Y
and
−Y
directions
and
those
of
the
third
Pauli
matrix,
the
+Z
and
−Z
directions.
The
dot
product
of
the
Pauli
vector
with
any
unit
vector
⃑N
yields
a
matrix
which
likewise
has
eigenvalues
+1
and
−1
and
a
pair
of
eigenvectors;
the
eigenvector
with
positive
eigenvalue
"encodes"
the
+N
direction
and
the
eigenvector
with
negative
eigenvalue
"encodes"
the
−N
direction.
The
dot
product
of
any
two
such
"encoded"
directions
yields
the
probability
amplitude
that
the
spin
of
an
electron
prepared
in
the
first
direction
will
collapse
to
the
second
direction
when
measured
along
that
second
direction.
Quizzes for review
The eigenvectors of the first Pauli matrix encode
— as it were — the +X and −X directions. Likewise, the eigenvectors of the second Pauli matrix encode
the +Y and −Y directions and those of the third Pauli matrix, the +Z and −Z directions. The dot product of the Pauli vector with any unit vector ⃑N yields a matrix which likewise has eigenvalues +1 and −1 and a pair of eigenvectors; the eigenvector with positive eigenvalue encodes
the +N direction and the eigenvector with negative eigenvalue encodes
the −N direction. The dot product of any two such encoded
directions yields the probability amplitude that the spin of an electron prepared in the first direction will collapse to the second direction when measured along that second direction.
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English - English
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