Poschl-Teller potentials based solution to Hilbert's tenth problem

Hypercomputers compute functions or numbers, or in general solve problems that cannot be computed or solved by a Turing machine. An adaptation of the hypercomputing quantum algorithm proposed by Tien D. Kieu is presented, to the dynamic algebra su (1, 1) performed on the Pöschl-Teller potentials. The classically incomputable problem that is solved with this hypercomputing algorithm is Hilbert's tenth problem. It is pointed out that a fundamental mathematical condition for these algorithms is the existence of an irreducible infinite dimensional unit representation of low-dimension algebras that admit the construction of coherent states of the Barut-Girardello type. Additionally, the hypercomputational algorithm on the infinite potential box previously constructed by the authors is presented as a limiting case of the proposed algorithm on the Pöschl-Teller potentials.

• Autores: Sicard, Andrés; Ospina, Juan
• Fecha de publicación: 2006
• Institución: Universidad EAFIT
• Repositorio: Repositorio EAFIT
• Idioma: eng
• OAI Identifier: oai:repository.eafit.edu.co:10784/14552
• Acceso en línea: http://hdl.handle.net/10784/14552
• Palabra clave: Hypercomputing; Adiabatic Quantum Computing; Hilbert'S Tenth Problem; Hipercomputación; Computación Cuántica Adiabática; Décimo Problema De Hilbert
• License: Copyright (c) 2006 Andrés Sicard, Juan Ospina