We find that V is independent of x. Therefore, X(x) = C₁ , where C₁is a constant.

Therefore, ..................(2.125)

We observe that the potential has to be equal to V₀ at y = 0 and as the potential function becomes zero. Therefore, the y dependence can be expressed as an exponential function. Similarly, since V = 0 for z = 0 and z = d, the z dependence will be a sinusoidal function with k_z = k, k being a real number.

Therefore,                                                  .....................(2.126)

...............(2.127)

.........................(2.128)

Combining all these terms we can write:

, where C is a constant.

Using the condition that V(y,d) =0, we can write , n=1,2,3,....