- #1
UniPhysics90
- 16
- 0
This isn't actually a homework problem, but a problem from a book, but as it's quite like a homework problem I thought this forum was probably the best place for it.
Consider a system with one degree of freedom, described by the Hamiltonian formulation of classical mechanics in terms of the coordinate q, and the canonically conjugate momentum, p. A canonical transformation is applied, such that the transformed Hamiltonian is described in terms of the transformed coordinate Q and the transformed momentum P. Explain whether P will be canonically conjugate to Q, and how Poisson brackets may be used to check this.
P will be canonically conjugate to Q (it says so in a book!) and possibly that Poisson brackets will give a constant value (books seem to suggest either 0 or 1?). If anyone can explain this further I'd really appreciate it!
Thanks
Homework Statement
Consider a system with one degree of freedom, described by the Hamiltonian formulation of classical mechanics in terms of the coordinate q, and the canonically conjugate momentum, p. A canonical transformation is applied, such that the transformed Hamiltonian is described in terms of the transformed coordinate Q and the transformed momentum P. Explain whether P will be canonically conjugate to Q, and how Poisson brackets may be used to check this.
Homework Equations
The Attempt at a Solution
P will be canonically conjugate to Q (it says so in a book!) and possibly that Poisson brackets will give a constant value (books seem to suggest either 0 or 1?). If anyone can explain this further I'd really appreciate it!
Thanks