In analogy with the one-dimensional problem, the condition at x = 0 gives
f (0) = 0, which requires B = 0 in Eq. 5.40. Similarly, the condition at y = 0
gives g(0) = 0, which requires D = 0. The condition f (L) = 0 requires that
sin kxL = 0, and thus that kxL be an integer multiple of π; the condition g(L) = 0
similarly requires that kyL be an integer multiple of π. These two integers do not
necessarily need to be the same, so we call them nx and ny. Making all these
substitutions into Eq. 5.39, we obtain