Solving PDEs?



My friend has had good success with Maxima on his project. He makes the 
comment --

  It seems Maxima is not able to handle partial differential equations 
(with several variables),
  only ordinary differential equations. Mathematica and Maple have the 
reqired packages,
  but are mainly tailored for mechanical and engineering applications.

  Quantum mechanics is too special (requires algebraic eigenvalues for 
example). I think
  if  feasable solutions of the Schr?dinger equation in cartesian 
coordinates existed, they
  would be describe in books, at least in  the outline. I know that any 
group tried to solve
  quantum mechanical equations numerically on a rectangular grid, but it 
was rather
  unprecise because the grid was not adopted to the centralsymmetric 
geometry.

Is he right about PDEs in Maxima? Have the packages he refers to been 
converted?
Are you familiar with the general solutions he is seeking?

Thank you again for your expertise.