Abstract: Starting from a set of completed eigenfunctions, we build a phenomenological formula under the rep-resentation principle, and then the completeness of eigenfunction of the Hermitian operators is proved by reduction to absurdity. This set of completed eigenfunctions of mechanical quantities can be projected onto the eigenfunctions of operator space, which gives the general proof of completeness of eigenfunctions of operators.

Key words: eigenfunction of Hermitian operator, reduction to absurdity, completeness, general proof