  The behaviour of quantum systems in non-inertial frames is revisited from the
point of view of affine coherent state (ACS) quantization. We restrict our
approach to the one-particle dynamics confined in a rotating plane about a
fixed axis. This plane is considered as punctured due to the existence of the
rotation center, which is viewed as a singularity. The corresponding phase
space is the affine group of the plane and the ACS quantization enables us to
quantize the system by respecting the affine symmetry of the true phase space.
Our formulation predicts the appearance of an additional quantum centrifugal
term, besides the usual angular momentum one, which prevents the particle to
reach the singular rotation center. Moreover it helps us to understand why two
different non-inertial Schr\"{o}dinger equations are obtained in previous
works. The validity of our equation can be confirmed experimentally by
observing the harmonic oscillator bound states and the critical angular
velocity for their existence.
