  We apply a wavefunction approach to study the charge 4$e$ superconductor. The
wavefunction takes a similar structure to the BCS wavefunction for charge 2$e$
superconductors. The mean-field Hamiltonian and the Green's functions of charge
4$e$ are constructed. The physical properties including the density of states,
gauge invariance, flux quantization and Josephson effects are systematically
studied. All these results form a microscopic description of the charge 4$e$ SC
and can be served as the hallmarks for experimental verifications.
