[ms physics]

السلام عليكم ورحمة الله وبركاته
اعزائي اريد اثباتات اقواس بواسون Poisson Brackets
Prove the flowing:
(1) [F, F] = 0
(2) [F, G] = - [G, F]
(3) [F, (G + g)]= [F,G] + [F,g]
(4) [F, G g] = [F,G]g + G[F,g]
علما بان The Poisson bracket of any two function F(q, p, t) and G(q, p, t) with
respect to the canonical variables (q, p)
وايضا
calculate the flowing
(1) [qj, qk], (2) [pj, pk]
(3) [qj, pk] (4) [qk, H]
بليز اريدها اليوم