  We address the problem of bounding rigorously the errors in the numerical
solution of the Kohn-Sham equations due to (i) the finiteness of the basis set,
(ii) the convergence thresholds in iterative procedures, (iii) the propagation
of rounding errors in floating-point arithmetic. In this contribution, we
compute fully-guaranteed bounds on the solution of the non-self-consistent
equations in the pseudopotential approximation in a plane-wave basis set. We
demonstrate our methodology by providing band structure diagrams of silicon
annotated with error bars indicating the combined error.
