Claim: For any function † (q,p,t), df Proof: df = dt af {f, H} + (4.62) Ət af af af Ət - %+%*+% = dt дрі
Claim: For any function † (q,p,t), df Proof: df = dt af {f, H} + (4.62) Ət af af af Ət - %+%*+% = dt дрі
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It says (in blue highlighted) that I will be of constant motion if I and H poisson commute.
Please show that this is true in detail.
Transcribed Image Text:Claim: For any function f(q, p,t),
Proof:
df
af
{f, H} +
(4.62)
dt
Ət
df
dt
=
af
дрі
af
af
·Pi +
-ġi +
Əqi
Ət
- 94 -
дf дн
дf ән
=
+
მp; მq; да дрі
af
= {ƒ,H} +
Ət
+
55
af
(4.63)
Ət
Isn't this a lovely equation! One consequence is that if we can find a function I (p,q)
which satisfy
{I, H} = 0
(4.64)
then I is a constant of motion. We say that I and H Poisson commute. As an example
of this, suppose that q; is ignorable (i.e. it does not appear in H) then
{pi, H}
(4.65)
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