 Home

Codex Wiki

List of universities

University of Oxford

Course of the University of Oxford

Undergraduate course of the University of Oxford

Physics course of the University of Oxford

Short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford

Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford

2012

For the canonical <Poisson bracket>, direct substitution of $F=q_i$ and $F=p_i$ gives
$$
\{q_i,G\}=\frac{\partial G}{\partial p_i},\qquad
\{p_i,G\}=-\frac{\partial G}{\partial q_i}.
$$
Therefore
$$
\sum_i\frac{\partial F}{\partial q_i}\{q_i,G\}
+\sum_i\frac{\partial F}{\partial p_i}\{p_i,G\}
=\sum_i\left(F_{q_i}G_{p_i}-F_{p_i}G_{q_i}\right)
=\boxed{\{F,G\}.}
$$
This expresses the bracket as a first-order derivative acting on $F$, with coefficients determined by $G$; it is the phase-space chain-rule form of the definition.

Solution

Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S7 / 2 / 1 / Solution

Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S7 / 2 / 1 / Solution

 Ancestors (12)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S7 / 2 / 1 / Solution

 Ancestors (12)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)