- #1

LCSphysicist

- 646

- 162

- Homework Statement
- Generating function

- Relevant Equations
- .

Prove directly that the transformation $$Q_{1} = q_{1}, P_{1} = p_{1} − 2p_{2}$$ $$Q_{2} = p_{2}, P_{2} = −2q_{1} − q_{2}$$ is canonical and find a generating functionSo the first part is easy and can be skipped here. I have some difficults regarding the second part, namely, the one that ask for the generator function.

My approach was to evaluate the object ##\sum_i p_i dq_i - P_i dQ_i##, i have read at MG Calkin that if this object can be written as a total differential ##dF##, this one is (can be) the generating function.

So, expandin the differential, i have got that ##\sum_i p_i dq_i - P_i dQ_i = d(p_2q_2 + 2p_2q_1) \implies F = F(P_2,p_2) = -p_2P_2##.

What do you think? is it ok?

My approach was to evaluate the object ##\sum_i p_i dq_i - P_i dQ_i##, i have read at MG Calkin that if this object can be written as a total differential ##dF##, this one is (can be) the generating function.

So, expandin the differential, i have got that ##\sum_i p_i dq_i - P_i dQ_i = d(p_2q_2 + 2p_2q_1) \implies F = F(P_2,p_2) = -p_2P_2##.

What do you think? is it ok?