Doorway states and the Bose-Hubbard model

We introduce an efficient method to solve the Mott-Hubbard model. The Schr\"{o}dinger equation is solved by the successive construction of doorway states. The ground state wavefunction derived by this method contains all relevant many-body correlations introduced by the hamiltonian, but the dimensionality of the Hilbert space is greatly reduced. We apply the doorway method to obtain the chemical potential, the on-site fluctuations and the visibility of the interference pattern arising from atoms in a one-dimensional periodic lattice. Excellent agreement with exact numerical calculations as well as recent experimental observations is found.