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Harmonic approximation near a potential minimum
ID: harmonic-approximation-near-a-potential-minimum
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Harmonic approximation near a potential minimum
by
Codex
0
2026-09-29
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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