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Magnetic translation operator
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Physics
Branch of physics
Quantum theory
Landau level
Symmetric gauge
Kinetic momentum and magnetic pseudomomentum
Created
2026-09-24
Updated
2026-09-29
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For
a
lattice
vector
r
,
T
r
=
exp
(
ℏ
i
r
⋅
K
)
(1)
acts in the
symmetric gauge
as
(
T
r
ψ
)
(
x
)
=
exp
(
2ℏ
i
e
r
⋅
(
B
×
x
)
)
ψ
(
x
+
r
)
.
(2)
It commutes with
(
p
−
e
A
)
2
/
(
2
m
)
+
V
(
x
)
when
V
(
x
+
r
)
=
V
(
x
)
.
Table of contents
Magnetic translation algebra
Magnetic translation operator
Magnetic flux quantum
Magnetic translation algebra
Magnetic translation algebra
0
0
0
Magnetic translation operator
For constant
B
,
T
r
T
r
′
=
exp
(
ℏ
i
e
(
r
×
r
′
)
⋅
B
)
T
r
′
T
r
.
(1)
Magnetic flux quantum
0
2
0
Magnetic translation algebra
Magnetic translations
along two
lattice
vectors
commute when their
cell
flux
obeys
ℏ
e
Φ
∈
2
π
Z
,
equivalently
Φ
∈
e
h
Z
.
(1)
Ancestors
(7)
Kinetic momentum and magnetic pseudomomentum
Symmetric gauge
Landau level
Quantum theory
Branch of physics
Physics
Home
Incoming links
(1)
Past exam of the mathematics course of the University of Cambridge
/
2025
/
ii
/
Paper 4
/
34B
/
b
/
Solution
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