Being encountered in various forms, phase-amplitude methods are powerful devices for a plethora of quantum-mechanical problems. In atomic and molecular collisions, the phase in the wavefunction of the Schrödinger equation is the principal ingredient for the computation of thermophysical and transport properties in a gas or in the condensed matter. In the current report, an original Lippmann-Schwinger-based formulation, addressing the absolute definition and calculation of phase functions and shifts, i.e., concepts instrumental in the calculation of such properties, is developed. This formulation, aside from being mathematically exact, is particularly well-suited for computations relevant to short, long and infinite range interactions, thereby offering evidence of its utility to a variety of molecular, physicochemical, or nuclear-engineering problems. Unsuspected linkages with the Milne phase are uncovered, encompassing not only all short and.infinite-range interactions in a unified framework but also the persistent ones, i.e., those in which the range is no longer a meaningful concept. Furthermore, a thoroughly improved, surprisingly simple and insightful model, which had formerly been developed for bound clusters (a single, loosely bound vibrational state in He2, Efimov-state calculations in He3, ...), but which at the time had failed to reproduce properties relevant to the He—He continuum, is proposed and applied to thermophysical and transport properties of helium. Finally, the concept of Bohm’s real and complex trajectory is introduced and applied to three distinct case-problems at the interface between a quantum and classical description: the dissipative harmonic oscillator, the bistability of NH3, and the rotation of a three-bladed bicyclooctane molecular rotator synthesized on the spot.