Can someone pleae tell me if I answered this right and if I am missing it or am I wrong. the molecule I have to do it for is picene

The model I was given is picene and I need to answer this question: 2. Show how the 2D-PIB Schroedinger equation can be separated into one differential equation in "x", and one diff eq in "y".+ 24(x) (y) + $" (y) E 2m p(y) Since the left side of the equation depends only on x and the right side depends only on y, both sides must be equal to a constant, which we denote as E, for the left side and Ey for the right side: + 24 (x) $(y) + (" (y) = Ex = Ey 2m p(y) Now, we have two separate equations: Ex 2m v(x) h2 0 (y ) 2m (y) = By These are the separated differential equations in the x-direction and y-direction, respectively, for the 2D PIB system. This separation allows us to solve the 2D problem by solving two 1D problems independently, making the problem more tractable