The intersection between dual potential and sl(2) algebraic spectral problems

Author:

Pannell William H.1ORCID

Affiliation:

1. School of Physics and Astronomy, University of Minnesota Twin-Cities, 116 Church St SE, Minneapolis, Minnesota 55455, USA

Abstract

The relation between certain Hamiltonians, known as dual, or partner Hamiltonians, under the transformation [Formula: see text] has long been used as a method of simplifying spectral problems in quantum mechanics. This paper seeks to examine this further by expressing such Hamiltonians in terms of the generators of sl(2) algebra, which provides another method of solving spectral problems. It appears that doing so greatly restricts the set of allowable potentials, with the only nontrivial potentials allowed being the Coulomb [Formula: see text] potential and the harmonic oscillator [Formula: see text] potential, for both of which the sl(2) expression is already known. It also appears that, by utilizing both the partner potential transformation and the formalism of the Lie-algebraic construction of quantum mechanics, it may be possible to construct part of a Hamiltonian’s spectrum from the quasi-solvability of its partner Hamiltonian.

Publisher

World Scientific Pub Co Pte Lt

Subject

Astronomy and Astrophysics,Nuclear and High Energy Physics,Atomic and Molecular Physics, and Optics

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