Most General form of Canonical Transformation

  • #1
kolawoletech
4
0
How do I go about finding the most general form of the canonical transformation of the form
Q = f(q) + g(p)
P = c[f(q) + h(p)]
where f,g and h are differential functions and c is a constant not equal to zero. Where (Q,P) and (q,p) represent the generalised cordinates and conjugate momentum in the new and old system
 

Answers and Replies

  • #2
vanhees71
Science Advisor
Insights Author
Gold Member
2021 Award
21,648
12,461
Isn't this "homework" of some kind? You should post it in the Homework and Coursework section! Anyway, here's some hint:

I'd try to determine constraints on the functions by evaluating the Poisson brackets which must be
$$\{Q,Q\}=\{P,P \}=0, \quad \{Q,P \}=1$$
in order to have a canonical transformation.
 
  • Like
Likes AlphaCentaury
  • #3
kolawoletech
4
0
I am done all that with certain kinds of relationship between (Q,P) and (q,p) but I am unable to do so with this general formula that does not give the function itself
 

Suggested for: Most General form of Canonical Transformation

Replies
6
Views
484
Replies
3
Views
255
Replies
4
Views
322
Replies
4
Views
165
Replies
9
Views
473
Replies
3
Views
1K
Replies
3
Views
254
Replies
3
Views
3K
Replies
8
Views
551
Top