  In a two-dimensional world a free quantum particle of vanishing angular
momentum experiences an attractive force. This force originates from a
modification of the classical centrifugal force due to the wave nature of the
particle. For positive energies the quantum anti-centrifugal force manifests
itself in a bunching of the nodes of the energy wave functions towards the
origin. For negative energies this force is sufficient to create a bound state
in a two-dimensional delta function potential. In a counter-intuitive way the
attractive force pushes the particle away from the location of the delta
function potential. As a consequence, the particle is localized in a
band-shaped domain around the origin
