In lattice Schrödinger picture, the wave functionals of the squeezed vacuum states of a free real scalar field in de Sitter space are constructed explicitly in momentum space by using the method of instantaneous Hamiltonian diagonalization. The modified power spectrum and particle production in the general mixed, squeezed initial states are also presented. For the massless minimally coupled scalar field which is relevant to slow roll inflationary models, we recover the power spectrum of scalar fluctuations for the squeezed vacuum states, and show that the evolution of the squeezed vacuum states exhibits an attractor behavior. The case of a massless conformally coupled scalar field is also discussed.