  We study the crossover of a finite one-dimensional (1D) bosonic ensemble from
weak to strong interactions in harmonic traps and multi-well potentials.
Although these systems are very common in experimental setups and have been
studied theoretically, an analytical description is lacking. We perform
Diffusion Quantum Monte Carlo calculations which we show to be in good
agreement with results from analytical functions that we construct to describe
these systems. For the harmonic trap we use the correlated-pair wave function
which we introduced in [1] considering here much larger atom numbers, going
beyond the few-body ensembles studied in \cite{brouzos}. We also investigate
double and triple wells, changing correspondingly the uncorrelated part of the
Ansatz to describe efficiently the single-particle behaviour. On-site effects
beyond mean-field and standard Bose-Hubbard calculations that appear in
densities being captured by our analytical functions are explored.
