Year: 2024
Type: article
Abstract: Rigged Hilbert spaces (RHSs) are the right mathematical context that include many tools used in quantum physics, or even in some chaotic classical systems. It is particularly interesting that in RHS, discrete and continuous bases, as well as an abstract basis and the basis of special functions and representations of Lie algebras of symmetries are used by continuous operators. This is not possible in Hilbert spaces. In the present paper, we study a model showing all these features, based on the one-dimensional Pöschl–Teller Hamiltonian. Also, RHS supports representations of all kinds of ladder operators as continuous mappings. We give an interesting example based on one-dimensional Hamiltonians with an infinite chain of SUSY partners, in which the factorization of Hamiltonians by continuous operators on RHS plays a crucial role.
Source: Axioms
Institutions: Instituto Politécnico Nacional, Universidad de Valladolid
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,728
Awards: G1090699031, G1175115578, G120905174, G2262748287, G24120701, G2601397997, G294895050, G300979063, G3166424744, G3480869486, G3681454997, G3860215346, G4030862296, G4042783231, G425668148, G464105488, G4694488986, G494616509, G5080475149, G5195188938, G5407845653, G5532355368, G7084143925, G7330179772, G7758289794, G8101614437, G8575893512
OpenAlex ID: W4405318067