  We use the density-matrix renormalization group method to investigate
ground-state and dynamic properties of the one-dimensional Bose-Hubbard model,
the effective model of ultracold bosonic atoms in an optical lattice. For fixed
maximum site occupancy $n_b=5$, we calculate the phase boundaries between the
Mott insulator and the `superfluid' phase for the lowest two Mott lobes. We
extract the Tomonaga-Luttinger parameter from the density-density correlation
function and determine accurately the critical interaction strength for the
Mott transition. For both phases, we study the momentum distribution function
in the homogeneous system, and the particle distribution and quasi-momentum
distribution functions in a parabolic trap. With our zero-temperature method we
determine the photoemission spectra in the Mott insulator and in the
`superfluid' phase of the one-dimensional Bose-Hubbard model. In the insulator,
the Mott gap separates the quasi-particle and quasi-hole dispersions. In the
`superfluid' phase the spectral weight is concentrated around zero momentum.
