To extend the given equation to two dimensions, we can simply add another dimension, let’s say “y,” to the equation. We can write the two-dimensional equation as:
Ψ_shifted(x, y) = (√(2/L) * cos(π(x - 0.5)/L) * cos(π(y - 0.5)/L)) / L^2
Here, we have multiplied the equation with the cosine of “y” in addition to the cosine of “x”. The equation still satisfies the condition of 0 ≤ x, y ≤ 1.