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Template
:
Pictures in quantum mechanics
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Evolution of:
Picture
(
v
t
e
)
Schrödinger
(S)
Heisenberg
(H)
Interaction
(I)
Ket state
|
ψ
S
(
t
)
⟩
=
e
−
i
H
S
t
/
ℏ
|
ψ
S
(
0
)
⟩
{\displaystyle |\psi _{\rm {S}}(t)\rangle =e^{-iH_{\rm {S}}~t/\hbar }|\psi _{\rm {S}}(0)\rangle }
constant
|
ψ
I
(
t
)
⟩
=
e
i
H
0
,
S
t
/
ℏ
|
ψ
S
(
t
)
⟩
{\displaystyle |\psi _{\rm {I}}(t)\rangle =e^{iH_{0,\mathrm {S} }~t/\hbar }|\psi _{\rm {S}}(t)\rangle }
Observable
constant
A
H
(
t
)
=
e
i
H
S
t
/
ℏ
A
S
e
−
i
H
S
t
/
ℏ
{\displaystyle A_{\rm {H}}(t)=e^{iH_{\rm {S}}~t/\hbar }A_{\rm {S}}e^{-iH_{\rm {S}}~t/\hbar }}
A
I
(
t
)
=
e
i
H
0
,
S
t
/
ℏ
A
S
e
−
i
H
0
,
S
t
/
ℏ
{\displaystyle A_{\rm {I}}(t)=e^{iH_{0,\mathrm {S} }~t/\hbar }A_{\rm {S}}e^{-iH_{0,\mathrm {S} }~t/\hbar }}
Density matrix
ρ
S
(
t
)
=
e
−
i
H
S
t
/
ℏ
ρ
S
(
0
)
e
i
H
S
t
/
ℏ
{\displaystyle \rho _{\rm {S}}(t)=e^{-iH_{\rm {S}}~t/\hbar }\rho _{\rm {S}}(0)e^{iH_{\rm {S}}~t/\hbar }}
constant
ρ
I
(
t
)
=
e
i
H
0
,
S
t
/
ℏ
ρ
S
(
t
)
e
−
i
H
0
,
S
t
/
ℏ
{\displaystyle \rho _{\rm {I}}(t)=e^{iH_{0,\mathrm {S} }~t/\hbar }\rho _{\rm {S}}(t)e^{-iH_{0,\mathrm {S} }~t/\hbar }}