# Homework Help: Canonical Transformations

1. Apr 5, 2015

### photomagnetic

1. The problem statement, all variables and given/known data
Show that x = 2qa/sin(T) and p = 2qa.cos(T) is a canonical transformation
into new coordinates T and momentum q.

2. Relevant equations

3. The attempt at a solution
It looks easy, I've tried matrix/jacobi method, and symplectic method. But these two seem to be not canonical. Am I missing something? The question doesn't give anything else. Do I have to find a generating function to prove that they are canonical? But then it'd would be silly, because the professor is very clear about these things. If he wanted to see a F generating function he would have said so.

2. Apr 6, 2015

### MarcusAgrippa

Clue: do you have any theorems that provide necessary and sufficient conditions for a transformation to be canonical?

3. Apr 7, 2015

### photomagnetic

I re-correct myself, the prof. is an *******. He hadn't mentioned that we had to use a generating function. now I got it. thanks anyway.

4. Apr 7, 2015

### MarcusAgrippa

That's not nice. I'm sure your prof is a very nice fellow.

Incidentally, there are several different methods that you might have used to show that the given transformation is canonical.

5. Apr 7, 2015

### photomagnetic

Yeah not telling which method we "must" use is not nice either.
Anyway after trying to do 3 hws each week, and spending a huge chunk of time,
people can get mad. Also no need to be politically correct here.