The Pauli spin in quantum mechanics are A = 0 1 1 0 , B = 0 − i i 0 , C = 1 0 0 − 1 (You Will probably find these called m σ x , σ y , σ z , in your quantum mechanics texts.) Show that A 2 =B 2= C 2 a unit matrix. Also show that any two of these matrices anticommute, that is, AB = —BA, etc. Show that the commutator Of A and B, that is, AB — BA, is 2iC, and similarly for other pairs in cyclic order.
The Pauli spin in quantum mechanics are A = 0 1 1 0 , B = 0 − i i 0 , C = 1 0 0 − 1 (You Will probably find these called m σ x , σ y , σ z , in your quantum mechanics texts.) Show that A 2 =B 2= C 2 a unit matrix. Also show that any two of these matrices anticommute, that is, AB = —BA, etc. Show that the commutator Of A and B, that is, AB — BA, is 2iC, and similarly for other pairs in cyclic order.
The Pauli spin in quantum mechanics are
A
=
0
1
1
0
,
B
=
0
−
i
i
0
,
C
=
1
0
0
−
1
(You Will probably find these called m
σ
x
,
σ
y
,
σ
z
, in your quantum mechanics texts.) Show that A2=B2=C2 a unit matrix. Also show that any two of these matrices anticommute, that is, AB = —BA, etc. Show that the commutator Of A and B, that is, AB — BA, is 2iC, and similarly for other pairs in cyclic order.
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