  We have discovered a class of dynamically stable coherent states for motion
on the half-line. The regularization of the half-line boundary and the
consequent quantum motion are expounded within the framework of covariant
affine quantization, although alternative approaches are also feasible. The
former approach is rooted in affine coherent states and offers a consistent
semiclassical representation of quantum motion. However, this method has been
known to possess two shortcomings: (a) the dependence of affine coherent states
on the choice of a vector, denoted as 'fiducial vector' (which remains
unspecified), introduces significant arbitrariness in boundary regularization,
and (b) regardless of the choice of 'fiducial vector,' affine coherent states
fail to evolve parametrically under the Schr\"odinger equation, thus limiting
the accuracy of the semiclassical description. This limitation, in particular,
hampers their suitability for approximating the evolution of compound
observables. We demonstrate that a distinct and more refined definition of
affine coherent states can simultaneously address both of these issues. In
other words, these new affine coherent states exhibit parametric evolution only
when the 'fiducial vector,' denoted as $|\psi_0>$, possesses a highly specific
character, such as being an eigenstate of a well-defined Hamiltonian. Our
discovery holds significant relevance in the field of quantum cosmology,
particularly in scenarios where the positive variable is the scale factor of
the universe, and its regularized motion plays a crucial role in avoiding the
big-bang singularity.
