Question 705048

The Hamiltonian is $H = \frac{p^2}{2} + \frac{q^2}{2}$. The Poisson bracket is $\{A, H\} = \frac{\partial A}{\partial q}\frac{\partial H}{\partial p} - \frac{\partial A}{\partial p}\frac{\partial H}{\partial q} = (\frac{i}{\sqrt{2}})(p) - (\frac{1}{\sqrt{2}})(q) = i(\frac{p+iq}{\sqrt{2}}) = iA$.