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Proof of Ehrenfest theorem from the Schrodinger equation
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Ehrenfest theorem
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Differentiating
⟨
ψ
∣
O
∣
ψ
⟩
and using
i
ℏ∣
ψ
˙
⟩
=
H
∣
ψ
⟩
and its adjoint gives
d
t
d
⟨
O
⟩
=
ℏ
i
⟨[
H
,
O
]⟩
+
⟨
∂
t
∂
O
⟩
.
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Ehrenfest theorem
Quantum mechanics
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Physics
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