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Chinese Physics Letters

Semi-unitary Transformation Induced Supersymmetric Partner Hulthen System

Jiu-An Zhang, Gui-rong Ma, Jian-zu Zhang A B

Published Jul 1, 1996• 0 citations
Publisher

Abstract

The supersymmetric partner system of Hulthen system in the s state is obtained by using a semi-unitary transformation. The physical foundation of applications of semi-unitary transformation to supersymmetric quantum mechanics is explored.
DOI
10.1088/0256-307x/13/7/002

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Physical Review A•Dec 1, 1996•1 citation
The concept of supersymmetry developed in particle physics has been applied to various fields of modern physics. In quantum mechanics, the supersymmetric systems refer to the systems involving two supersymmetric partner Hamiltonians, whose energy levels are degeneracy except one of the systems has an extra ground state possibly, and the eigenstates of the partner systems can be mapped onto each other. Recently, an interferometric scheme has been proposed to show this relationship in ultracold atoms [Phys. Rev. A 96 043624 (2017)]. Here this approach is generalized to linear optics for observing the supersymmetric dynamics with photons. The time evolution operator is simulated approximately via Suzuki–Trotter expansion with considering the realization of the kinetic and potential terms separately. The former is realized through the diffraction nature of light and the later is implemented using a phase plate. Additionally, we propose an interferometric approach which can be implemented perfectly using an amplitude alternator to realize the non-unitary operator. The numerical results show that our scheme is universal and can be realized with current technologies.
It is shown that in supersymmetric quantum mechanics the superpartner Hamiltonian H+{\mathit{H}}_{+}H+​ is related to the Hamiltonian ${\mathit{H}}_{\mathrm{\ensuremath{-}}}$ by a semiunitary transformation. The properties of the semiunitary transformation are discussed. \textcopyright{} 1996 The American Physical Society.