An Algebraic Model for Quantum Unstable States

Sebastian Fortin, Manuel Gadella (), Federico Holik, Juan Pablo Jorge and Marcelo Losada
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Sebastian Fortin: CONICET, Universidad de Buenos Aires, Buenos Aires 1428, Argentina
Manuel Gadella: Departamento de Física Teórica, Atómica y Optica, Universidad de Valladolid, Paseo Belén 7, 47011 Valladolid, Spain
Federico Holik: Instituto de Física La Plata, UNLP, CONICET, Facultad de Ciencias Exactas, La Plata 1900, Argentina
Juan Pablo Jorge: Facultad de Filosofía y Letras, Universidad de Buenos Aires, Puan 480, Buenos Aires 1428, Argentina
Marcelo Losada: Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, Av. Medina Allende s/n, Córdoba 5000, Argentina

Mathematics, 2022, vol. 10, issue 23, 1-21

Abstract: In this review, we present a rigorous construction of an algebraic method for quantum unstable states, also called Gamow states. A traditional picture associates these states to vectors states called Gamow vectors. However, this has some difficulties. In particular, there is no consistent definition of mean values of observables on Gamow vectors. In this work, we present Gamow states as functionals on algebras in a consistent way. We show that Gamow states are not pure states, in spite of their representation as Gamow vectors. We propose a possible way out to the construction of averages of observables on Gamow states. The formalism is intended to be presented with sufficient mathematical rigor.

Keywords: Gamow states; algebras of observables; time evolution of states (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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