State and prove Liouville's Theorem. (q.p+dp) B р q` speed A (an) ↑p (q +dq.p+dp) C D (q dq,p)

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State and prove Liouville's Theorem.
(q.p+dp)
B
р
0
q
speed
i. e.
df
dt
A
(q.p)
N
-
Account to Liouville's Theorem we define
the number of point one unit volume of phase
space as density p, then account to this theorem
the density of point remain constant with time.
V
= :0
p = constant
(q +dq.p+dp)
C
↑p
(speed)
q
D
(q dq,p)
Transcribed Image Text:State and prove Liouville's Theorem. (q.p+dp) B р 0 q speed i. e. df dt A (q.p) N - Account to Liouville's Theorem we define the number of point one unit volume of phase space as density p, then account to this theorem the density of point remain constant with time. V = :0 p = constant (q +dq.p+dp) C ↑p (speed) q D (q dq,p)
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