  We apply a path integral variational approach to obtain analytical
expressions for condensate wave functions of an ultracold, interacting trapped
Bose gases. As in many recent experiments, the particles are confined in a 1D
or 3D harmonic oscillator trap which is superimposed by a periodic potential in
one direction. Based on the first order cumulant expansion with respect to a
harmonic trial action, and emplyoing a mean-field approximation, optimal
variational parameters are obtained by minimizing an analytical expression for
the ground state energy. Our largely analytical results for energy and
condensate wave function are in good agreement with fully numerical
calculations based on the Gross-Pitaevskii equation.
