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Adiabatic particle between moving parallel walls
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Classical mechanics
Hamiltonian mechanics
Integrable Hamiltonian system
Action-angle variables
Action variable
Adiabatic invariance of the action
Created
2026-09-24
Updated
2026-09-24
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For
a
one-dimensional particle of
energy
E
between walls separated by
L
, the unnormalized
action
is
I
=
∮
p
d
q
=
2
L
2
m
E
.
(1)
Adiabatic conservation gives
E
(
t
)
L
(
t
)
2
=
constant
.
Ancestors
(9)
Adiabatic invariance of the action
Action variable
Action-angle variables
Integrable Hamiltonian system
Hamiltonian mechanics
Classical mechanics
Branch of physics
Physics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2023
/
ii
/
Paper 4
/
8D
/
Solution
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