- 2 For F And G Which Are Functions Of The Phase Space Variables 91 9m Pz Pn The Poisson Brackets Are Defined A 1 (66.29 KiB) Viewed 62 times
2. For f and g which are functions of the phase space variables (91,...9m; Pz....Pn), the Poisson brackets are defined as follows raf og af og ӘР, дail V.81 = ( ਨੂੰ, a) Consider the three functions f = f(x,P:). g= g(x.Px), and h =h(x, Px) and the two constants a and b. 1. Using the definition of the Poisson brackets, show that th, 20) = 0, (ht , af + bg] = a[h, fl + b[h,8). .gh) = 1.81h+8Vf.h). (10 marks) 2. Using the results above and the other properties of the Poisson brackets, calculate (Px, ly, P,x]]. (4 marks) b) For a generic Hamiltonian H(qı, P.) where i = 1,2,...11. prove 4. = 19,H) P = [P,HG (6 marks)