University:
Santa Fe College
Course:
PHY 2004 | Applied Physics 1
Academic year:

2024
Views:

101

Pages:

6
Author:

Jabin F.

#Differential Relation for Fu(bi, Pi,t) -> Legendre transformation from Fy to Fu Fu(bi, Pi,t) = Fa(bi, Qi, t) + Qi Pi 3 -ve ১০ → so tve y H=H+Fy Pi ap at G.F. given C.T. to be found Steps write appropriate differential relation. → Differentiate given G.F. to abtain required relation b/w (91) (@P) C.T. given G.F. to be found Method(D wwse G.F. given in option and check wheather we can obtains given, C. T. relation ar nat. given CT. @=@(a,b,t) & P= P(a, bit) Method → write appropriate differential relation → Express L.H.S. of differential relation in terms of variables used in G.F. For this use given C.T. relation. → Integrate partially to get two values of generating function. → If two values are different, then combine the two results, keeping common terms only once P-103 →A canonical transformation relates the old coordinates (a, b) to the Q-37 new coordinates (Q, P) by relations Q=q^3 and P=P/qg. The corresponding time independent generating function (Q, P) is Solution given C.T. ⇒ Q=q^3 and P=P/qg for F(Q, P), the differential relations are Q=∂F/∂P and P=∂F/∂Q.