I'm trying to calculate the probability of finding an electron in a cubic infinite well with a triple integral as follows:

Integrate[((2/L)^(3/2)

Sin[(2 pi x)/L] Sin[(pi y)/L] Sin[(pi z)/L])^2, {x, 0, L}, {y,

L/3, 2 L/3}, {z, 0, L}]

For some reason, I'm getting this error:

*Integrate::ilim: "Invalid integration variable or limit(s) in {(2\L)/3,L/3,(2\L)/3}"*

According to my sources, I should be getting a numerical answer of 0.609. Do I have to do something special to the variable 'L'?

Thank you in advance!