Gradient of multiparticle wavefunction

[confused_man]

Hi everyone,

This might belong in the quantum mechanics section, so I apologize if I placed this thread in the wrong place.

My question is: how do I calculate the gradient of a multiparticle wavefunction? For example, suppose that a wavefunction [tex]\psi[/tex] describing the probability amplitude for two particles with coordinates [tex](r_1,\phi_1)[/tex] and [tex](r_2,\phi_2)[/tex]:

[tex]
\psi = r_1r_2e^{i(\phi_1+\phi_2)}
[/tex]

and I want to find the gradient of [tex]\psi[/tex]. Is this even possible? What about the curl?

Thanks!

 

[smallphi]

Your notation implies that each particle position is specified by two coordinates which look like polar coordinates. Then, the wave function is a function of the 4 particle coordinates and the time. You can find two gradients, with respect to coordinates of particle 1 or with respect to coordinates of the second particle. Just find somewhere the expression of the components of the gradient vector in terms of the partial derivatives of the function and compute those.

You can't find the curl of the wave function since it is not a vector valued function, the curl operates only on vectors.