Frank Castle
- 579
- 23
In literature I have read it is said that the Hamiltonian ##H## is the generator of time translations. Why is this the case? Where does this statement derive from?
Does it follow from the observation that, for a given function ##F(q,p)##, $$\frac{dF}{dt}=\lbrace F,H\rbrace +\frac{\partial F}{\partial t}$$ In particular, if ##F## is not explicitly dependent on time, then $$\frac{dF}{dt}=\lbrace F,H\rbrace $$ Or is there more to it?
Does it follow from the observation that, for a given function ##F(q,p)##, $$\frac{dF}{dt}=\lbrace F,H\rbrace +\frac{\partial F}{\partial t}$$ In particular, if ##F## is not explicitly dependent on time, then $$\frac{dF}{dt}=\lbrace F,H\rbrace $$ Or is there more to it?