We present detailed ab initio density functional calculations of equilibrium atomic geometry, electronic states, and chemical bonding for the adsorption of the elemental Sn atoms on the Ge(111)-(3 x 3) surface. Three different possible models: (i) IDA model (inequivalent-two-down Sn atoms), (ii) 1U2D model (one-up Sn atom, two-equivalent-down Sn atoms), and (iii) 2U1D model (two-up Sn atoms, one-down Sn atom) have been considered. From these three models, it has been found that the IDA and 1U2D models are energetically favorable than the third model. The energy difference between the IDA and 1U2D model is negligibly small. For the IDA model, the height difference between two down atoms in IDA model is significant. A total of three surface states originating from the Sn adatoms is determined. The results are in good agreement with the recent high-resolution photoemission and scanning tunneling microscopy experiments.