Abstract:
Gelfand triplets are used in Quantum Mechanics with a variety of purposes, including a rigorous presentation of the Dirac Formulation of Quantum Mechanics, or a mathematical construction of certain structures linked to unstable quantum states, such as Gamow vectors. In addition, Gelfand triplets permit the combination of a series of structures commonly used in quantum textbooks, such as discrete and continuous basis or other features. Here, we present a limited number of examples thereof. Gelfand triplets will serve as a support of representations in terms of continuous operators of some examples of Lie algebras.