u[n_,x_]=Sqrt[2] Sin[n Pi x]
psi12[x_,y_]=u[1,x]u[2,y]
psi21[x_,y_]=u[2,x]u[1,y]

psiA=(Sqrt[2]psi12[x,y]+psi21[x,y])/Sqrt[3]
psiB=(psi12[x,y]-Sqrt[2] psi21[x,y])/Sqrt[3]

psiB /. {x->1/3,y->1/4}
Out[6]= 0

N[psiA^2] /. {x->1/3,y->1/4}
Out[7]= 4.5

ContourPlot[psiA^2,{x,0,1},{y,0,1},PlotPoints->100,ContourLines->False]
ContourPlot[psiB^2,{x,0,1},{y,0,1},PlotPoints->100,ContourLines->False]

Show[Graphics[{{RGBColor[1,0,0],Disk[{1/3, 1/4},.02]}}]]
Show[%8,%]
Show[%9,%%]
Show[GraphicsArray[{%%,%}]]

Export["t304#9.pdf",%]
