  Scattering off a potential is a fundamental problem in quantum physics. It
has been studied extensively with amplitudes derived for various potentials. In
this article, we explore a setting with no potentials, where scattering occurs
off a junction where many wires meet. We study this problem using a
tight-binding discretization of a star graph geometry -- one incoming wire and
$M$ outgoing wires intersecting at a point. When an incoming wave scatters, one
part is reflected along the same wire while the rest is transmitted along the
others. Remarkably, the reflectance increases monotonically with $M$, i.e., the
greater the number of outgoing channels, the more the particle bounces back. In
the $M \rightarrow \infty$ limit, the wave is entirely reflected back along the
incoming wire. We rationalize this observation by establishing a quantitative
mapping between a junction and an on-site potential. To each junction, we
assign an equivalent potential that produces the same reflectance. As the
number of wires ($M$) increases, the equivalent potential also increases. A
recent article by one of us has drawn an equivalence between junctions and
potentials from the point of view of bound state formation. Our results here
show that the same equivalence also holds for scattering amplitudes. We verify
our analytic results by simulating wavepacket motion through a junction. We
extend the wavepacket approach to two dimensions where analytic solutions
cannot be found. An incoming wave travels on a sheet and scatters off a point
where many sheets intersect. Unlike in 1D, the equivalent potential is
momentum-dependent. Nevertheless, for any given momentum, the equivalent
potential grows monotonically with the number of intersecting sheets. Our
findings can be tested in ultracold atom setups and semiconductor structures.
