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Principles of Quantum Mechanics
· Problem 14.3.6
Spin — R. Shankar
Physics — Quantum Mechanics · spin-rotation-operator
Problem
(1) Argue that
∣
n
^
,
+
⟩
=
U
[
R
(
ϕ
k
)
]
U
[
R
(
θ
j
)
]
∣
s
z
=
ℏ
/
2
⟩
|\hat{n}, +\rangle = U[R(\phi\mathbf{k})]U[R(\theta\mathbf{j})]|s_z = \hbar/2\rangle
∣
n
^
,
+
⟩
=
U
[
R
(
ϕ
k
)]
U
[
R
(
θ
j
)]
∣
s
z
=
ℏ/2
⟩
. (2) Verify by explicit calculation.
Related theory
Rotation Operator Identity Exponential Form Via Taylor Series
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