# Just plain dont know what to do or how to even start

1. Sep 20, 2007

### Phymath

1. The problem statement, all variables and given/known data
Well i've been working on these problems for the last 4 hours and still nothing...and out of despairation i turn to you all.

It has to do with Canonical transformations of the Hamiltonian:
1) Consider a type 1 generating function (F(q,Q,t)) where the following must be satisfied
$$p = \frac{\partial{F}}{\partial{q}} \ P = -\frac{\partial{F}}{\partial{Q}} \$$
show that for a single degree of freedom the possion bracket [Q,P] = 1 (aka canonical) now ive been able to show it is 0 obviously wrong and yes it makes use of many different forms of differentials any help on this would help

2) For Two particles interact via a central potential V(r1-r2) the H is
$$H= \frac{p_1^2}{2m_1}+\frac{p_2^2}{2m_2}+V(r_1-r_2)$$

$$Q = \frac{m_1 r_1+m_2 r_2}{M = m_1+m_2}, P = p_1+p_2$$

$$q= r_1 - r_2, \ p = \frac{m_2 p_1-m_1 p_2}{M}$$

this one im really not sure about, however i think the transformation is type 3 so that may help doing that what does anyone think? any help is always awesome.

show that the transformation is canonical

2. Relevant equations
$$[Q,P] = \frac{\partial{Q}}{\partial{q}}\frac{\partial{P}}{\partial{p}}-\frac{\partial{P}}{\partial{q}}\frac{\partial{Q}}{\partial{p}}$$

Last edited: Sep 20, 2007