Particle in a box

L = 1.; n =3.;
Plot [(2/L) (Sin [n Pi x / L])^2 , {x, 0, L},
Frame->True]

Integrate [(2/L) (Sin [2 Pi x / L])^2 , {x, 0, L/4}]

A 2-d box

DensityPlot[ (2/L) (Sin [2 Pi x / L])^2 (2/L) (Sin [2 Pi y / L])^2, {x, -2, 2}, {y, -2, 2}]

This is not a very helpful plot.  We may have to change two options: Plot Points and Mesh

DensityPlot[ (2/L) (Sin [2 Pi x / L])^2 (2/L) (Sin [2 Pi y / L])^2, {x, -2, 2}, {y, -2, 2},PlotPoints->500,Mesh->False]

Another helpful plot is ContourPlot

ContourPlot[ Sin[x y], {x, -2, 2}, {y, -2, 2}]