If there was a deviation between the experimentally calculated values and theoretical determination done by DFT calculation, then what is the credibility of the predicted properties like magnetic and electrical properties?

(From lecture notes - Band Gap ) In this scenario , I am trying to calculate two eigen functions of upper and lower band at the band edge $\frac{g}{2}$ for brillouin zone extending from $\frac{-g}{2}$ to $\frac{g}{2}$ for the eigen matrix given in picture above. if we were to calculate $\psi_{\f...