1. Nov 21, 2009

### luisgml_2000

1. The problem statement, all variables and given/known data
I'm asked to prove that if the Hamilton Jacobi equation is separable in certain coordinates then the system is integrable, that is, there exist $$n$$ integrals of motion in involution.

2. Relevant equations

3. The attempt at a solution

If the H-J equation

$$H\left(q^i,\frac{\partial G}{\partial q^i}\right)=-\frac{\partial G}{\partial t}$$

is separable then it means that

$$G=T(t)+Q_1(q^1)+\ldots+Q_n(q^n)$$

At first I thought that $$Q_i$$ would be the integrals of motion but later I realized that is not the case. What can I do next?

Thanks