Animation of the two dimension Particle in a box

Movie

<<Graphics`Animation`

?Animate

Lx=2;nnx=3;T=20;
Ly=2;nny=3;vel=(1/15);

w = N[(vel π) (Sqrt[(nnx/Lx)^2 + (nny/Ly)^2])]
T = N[2 π/w]

About 21 frames seem to work.

Animate[
        Plot3D[
              Sqrt[4/(Lx Ly)] Cos[(vel Pi) 
              (Sqrt[(nnx/Lx)^2 + (nny/Ly)^2] n )] 
              Sin[ Pi nnx x/Lx]
              Sin[ Pi nny y/Ly],
              {x,0,Lx},{y,0,Ly},PlotPoints->25,
               PlotRange->{-1,1},Boxed->False],
        {n,0,T},Frames->16
       ]