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. Claim: For any function f(q, p,t),Proof:dfaf{f, H} +(4.62)dtƏtdfdt=afдріafaf·Pi +-ġi +ƏqiƏt- 94 -дf дндf ән=+მp; მq; да дріaf= {ƒ,H} +Ət+55af(4.63)ƏtIsn'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 exampleof this, suppose that q; is ignorable (i.e. it does not appear in H) then{pi, H}(4.65)

Answered: Image /qna-images/answer/aea752ce-7e6c-435f-a27c-49fcb37ae827.jpg

Answered: Claim: For any function † (q,p,t), df…

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Claim: For any function † (q,p,t), df Proof: df = dt af {f, H} + (4.62) Ət af af af Ət - %+%*+% = dt дрі