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quantum mechanics
Heisenberg Picture
d
d
t
A
H
=
1
i
ℏ
[
A
H
,
H
]
+
(
∂
A
H
∂
t
)
\small {d \over d t}A_H = \frac{1}{i\hbar}[A_H, H] + \left(\frac{\partial A_H}{\partial t}\right)
d
t
d
A
H
=
i
ℏ
1
[
A
H
,
H
]
+
(
∂
t
∂
A
H
)
Schrodinger's Equation
i
ℏ
∂
∂
t
Ψ
(
x
,
t
)
=
[
−
ℏ
2
2
m
∂
2
∂
x
2
+
V
(
x
,
t
)
]
Ψ
(
x
,
t
)
\scriptsize i\hbar\frac{\partial}{\partial t}\Psi(x,t) = \left[-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} + V(x,t)\right]\Psi(x,t)
i
ℏ
∂
t
∂
Ψ
(
x
,
t
)
=
[
−
2
m
ℏ
2
∂
x
2
∂
2
+
V
(
x
,
t
)
]
Ψ
(
x
,
t
)