Hello everyone, I am given the inital hamiltonian H = (1/2)*(px2x4 - 2iypy + 1/x2) and the transformed hamiltonian K = (1/2)*(Px2 + Py2 + X2 + Y2) and I'm supposed to show there exists a canonical transformation that transforms H to K and find it. I don't know how to solve problems of this sort. I can find the canonical transformation given the generating function so I started with the equation K = H + ∂F/∂t where F is the generating function of the second kind and replaced the X, Y from K with ∂F/∂Px, ∂F/∂Py and the px, py from H with ∂F/∂x, ∂F/∂y to get a partial differential equation for the function F(x, y, Px, Py, t). Assuming a separable solution I solve the equation and obtain a generating function F but it's impossible to get transformation equations from this F because the solution is separable. Also I can't make sense of the constants of integrations in this situation. How does one deal with these kind of problems? Any help is appreciated!