Three examples of quantum dynamics on the half-line with smooth bouncing

Understand

This article is an introductory presentation of the quantization of the half-plane based on affine coherent states (ACS).

• The half-plane is viewed as the phase space for the dynamics of a positive physical quantity evolving with time, and its affine symmetry is preserved due to the covariance of this type of quantization.
• We promote the interest of such a procedure for transforming a classical model into a quantum one, since the singularity at the origin is systematically removed, and the arbitrariness of boundary conditions can be easily overcome.
• We explain some important mathematical aspects of the method.