  The quantum mechanical three-body problem is a source of continuing interest
due to its complexity and not least due to the presence of fascinating solvable
cases. The prime example is the Efimov effect where infinitely many bound
states of identical bosons can arise at the threshold where the two-body
problem has zero binding energy. An important aspect of the Efimov effect is
the effect of spatial dimensionality; it has been observed in three dimensional
systems, yet it is believed to be impossible in two dimensions. Using modern
experimental techniques, it is possible to engineer trap geometry and thus
address the intricate nature of quantum few-body physics as function of
dimensionality. Here we present a framework for studying the three-body problem
as one (continuously) changes the dimensionality of the system all the way from
three, through two, and down to a single dimension. This is done by considering
the Efimov favorable case of a mass-imbalanced system and with an external
confinement provided by a typical experimental case with a (deformed) harmonic
trap.
