  We develop a model to describe the motional (i.e., external degree of
freedom) energy spectra of atoms trapped in a one-dimensional optical lattice,
taking into account both axial and radial confinement relative to the lattice
axis. Our model respects the coupling between axial and radial degrees of
freedom, as well as other anharmonicities inherent in the confining potential.
We further demonstrate how our model can be used to characterize lattice light
shifts in optical lattice clocks, including shifts due to higher multipolar
(magnetic dipole and electric quadrupole) and higher order
(hyperpolarizability) coupling to the lattice field. We compare results for our
model with results from other lattice light shift models in the literature
under similar conditions.
