The behavior of deep level wavefunctions induced by short range defect potential is investigated when the energy difference ε between the defect state and the band edge is very small. When ε→0, the wavefunctions tend to expand in real space and concentrate in k space when some symmetric matching condition is satisfied. A specific scheme is developed for efficient and reliable numerical calculations of the deep level wavefunctions when ε is very small. For the case of A1 symmetric defect states near the bottom of the conduction band, for Si, when ε1 defect states near the top of the valance band, no concentration in k space occur since the A1 defect states mismatch to the Block states at valance band maxima.