Ground state quantum mechanics

Given the knowlegde of its kinematical class, a quantum system is completely characterized by the specification of a ground state. This provides a quantum formulation more general than the potential-based approach, handling situations where the ground state is a smooth function whereas the potential would be singular. Many results may be obtained directly from the ground state without needing to reconstruct the associated potential. Representations of the quantum algebra, generated by the ground state, describe all quantum states of the system and this approach is also useful as a tool to model observed physical phenomena and to find out what interactions are at play. The basic formalism and a variety of examples are included to illustrate the power of the ground state approach as a modelling tool for quantum systems.