Properties of shape-invariant tridiagonal Hamiltonians
Abstract
It has been established that a positive semi-definite Hamiltonian,, that has a tridiagonal matrix representation in a basis set, allows a definition of forward (and backward) shift operators that can be used to define the matrix representation of the supersymmetric partner Hamiltonian in the same basis. \ We show that if, additionally, the Hamiltonian has a shape invariant property, the matrix elements of the Hamiltonian are related in a such a way that the energy spectrum is known in terms of these elements. It is also possible to determine the matrix elements of the hierarchy of super-symmetric partner Hamiltonians. Additionally, we derive the coherent states associated with this type of Hamiltonians and illustrate our results with examples from well-studied shape-invariant Hamiltonians that also has tridiagonal matrix representation.
Keywords
Cite
@article{arxiv.1812.10749,
title = {Properties of shape-invariant tridiagonal Hamiltonians},
author = {Hashim A. Yamani and Zouhaïr Mouayn},
journal= {arXiv preprint arXiv:1812.10749},
year = {2018}
}