Question

For Poisson Brackets, which of the following statements are correct?
(A) [X, Y ] = −[Y, X]
(B) [X, X] = 0
(C) [X, Y + Z] = [X, Y ] + [Y, Z]
(D) [X, Y Z] = Y [X, Z] + [X, Y ]Z
Choose the correct answer from the options given below:

• (A) (B) and (D) only
• (A) (B) and (C) only
• (A) (B) (C) and (D)
• (B) (C) and (D) only

Hint:

Poisson brackets are essential for describing the time evolution of dynamical variables in classical mechanics.

Answer 1

The Correct Option is A

The Poisson bracket properties are well-defined in Hamiltonian mechanics and satisfy all the given relations:
(A) is true because the Poisson bracket is antisymmetric.
- (B) is true because any quantity commutes with itself. - (D) follows from the Leibniz rule.