Generalized Heisenberg algebras and k-generalized Fibonacci numbers

TL;DR

This paper generalizes recent results on Hamiltonians with eigenvalues as Fibonacci numbers to include k-generalized Fibonacci numbers, extending the mathematical framework to arbitrary integer k.

Contribution

It introduces a generalized approach to describe Hamiltonians with eigenvalues as k-generalized Fibonacci numbers, broadening the scope of previous specific cases.

Findings

Extended the mathematical description to arbitrary k

Connected Hamiltonian eigenvalues to k-Fibonacci sequences

Provided a unified framework for generalized Fibonacci eigenvalues

Abstract

It is shown how some of the recent results of de Souza et al. [1] can be generalized to describe Hamiltonians whose eigenvalues are given as k-generalized Fibonacci numbers. Here k is an arbitrary integer and the cases considered by de Souza et al. corespond to k=2.