- #1
csco
- 14
- 0
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!
How does one deal with these kind of problems?
Any help is appreciated!