  In modern fundamental theories there is consideration of higher dimensions,
often in the context of what can be written as a Schr\"odinger equation. Thus,
the energetics of bound states in different dimensions is of interest. By
considering the quantum square well in continuous $D$ dimensions, it is shown
that there is always a bound state for $0<D \le 2$. This binding is complete
for D \to 0 and exponentially small for D \to 2_-. For D>2, a finite-sized well
is always needed for there to be a bound state. This size grows like D^2 as D
gets large. By adding the proper angular momentum tail a volcano, zero-energy,
bound state can be obtained.
