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Harmonic approximation near a potential minimum
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Physics
Branches of physics
Quantum theory
Bloch's theorem
Tight binding
Created
2026-09-29
Updated
2026-10-14
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Near
a
nondegenerate minimum
x
0
,
a
smooth potential satisfies
V
(
x
)
=
V
(
x
0
)
+
2
1
V
′′
(
x
0
)
(
x
−
x
0
)
2
+
⋯
.
(1)
The localized levels are therefore approximately those of
a
harmonic oscillator
of
frequency
V
′′
(
x
0
)
/
m
; tunnelling broadens each level into
a
narrow band.
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Tight binding
Bloch's theorem
Quantum theory
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Physics
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Past exam of the mathematics course of the University of Cambridge
/
2020
/
ii
/
Paper 2
/
35C
/
b
/
ii
/
Solution
Past exam of the physics A course of the University of Cambridge
/
2018
/
Paper 2
/
Section A
/
A4
/
Solution
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