1. The problem statement, all variables and given/known data Given a wire with length a and square base b x b (where a >> b), show that the first 1700 (approximately) levels of the electron in the wire are identical for the one dimensional box, when a = 1m and b = 1mm. 2. Relevant equations I know that the allowed energies of a mass M in a 3D rectangular rigid box with sides a, b, and c are: E1 = ħ^2 * (Pi)^2 / 2M * (nx^2 / a^2 + ny^2 / b^2 + nz^2 / c^2) The energy of a 1-D box with length a is similar, being E2 = ħ^2 * (Pi)^2 / 2M * (n^2 / a^2) 3. The attempt at a solution For the purpose of this problem the energy of my wire is: E = ħ^2 * (Pi)^2 / 2M * (nx^2 / a^2 + ny^2 / b^2 + nz^2 / b^2) Now, I know by inspection and common sense that a long and very thing wire can be considered as a one dimensional system, which is used by the 1D Schrodinger equation. The problem is that I'm not quite sure how it works out mathematically. If a >> b, then doesn't this mean we generally ignore the a component of E1, since the b part basically dominates the energy? But all the same, you can't do that for the equation for the 1D box. It's all just a bit confusing for me.