dRic2
Gold Member
 560
 101
 Homework Statement

Give the proof of the equation
$$ H' = H + \frac { \partial S } { \partial t }$$
By proceeding as follow. Leave the time t as independent variable and consider a canonical transformation in which the time appears as a parameter. Then obtain the above relation by distinguishing between ##dS## in the canonical integral and ##\delta S## in the definition of canonical transformation. In the first case time is varied, in the second case not.
 Homework Equations

Canonical integral:
$$A = \int ( \sum p_i dq_i  Hdt)$$
Definition of canonical transformation:
$$ \sum p_i \delta q_i = \sum P_i \delta Q_i + \delta S$$
I'm stuck from the beginning. I though I understood the difference between ## \delta## and ##d##, but apparently I was wrong, because I don't know how to exploit it here...
Any hint would be greatly appreciated
Thank
Ric
Any hint would be greatly appreciated
Thank
Ric