Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Superpartner systems and semiunitary transformations in supersymmetric quantum mechanics

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

Published Dec 1, 1996• 1 citation
Publisher

Abstract

It is shown that in supersymmetric quantum mechanics the superpartner Hamiltonian ${\mathit{H}}_{+}$ 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.

DOI
10.1103/physreva.54.5418

Related papers

Features of Complex Supersymmetric Quantum Mechanics

Aishwarya Parthasarathi

The study of the non-Hermitian Hamiltonian systems within the framework of Supersymmetric Quantum mechanics (SUSY QM) has been carried out in literature in the last decade. Most of these potentials are either PT Symmetric or quasi-Hermitian in nature. But no formulation is advanced in literature to the study of general complex potentials within its framework. In this paper, using the complex phase space approach, we carry out the complexification of Supersymmetric Quantum Mechanics to enable the study of any general non-Hermitian Hamiltonian system within its framework. The commutation relations among its operators are enumerated and the underlying symmetry is discussed. The eigenvalues and eigenfunctions of the real and imaginary parts of superpartner Hamiltonians are also investigated.

•Sep 24, 2021•0 citations

Angular Momentum of Supersymmetric Non-isotropic Traps

Xu Qiang

A simple way to explain quantum behavior of supersymmetric non-isotropic traps is proposed in the framework of semiunitary formulation of supersymmetric quantum mechanics. Using semiunitary formulation we can simultaneously supersymmetrize the complete set of observables, especially including angular moment.

Communications in Theoretical Physics•Feb 15, 2001•0 citations

Supersymmetric η operators

Boris F Samsonov

Being chosen as a differential operator of a special form, the metric η operator has become unitary equivalent to a one-dimensional Hermitian Hamiltonian with a natural supersymmetric structure. We show that fixing the superpartner of this Hamiltonian permits us to determine both the metric operator and the corresponding non-Hermitian Hamiltonian. Moreover, under an additional restriction on the non-Hermitian Hamiltonian, it has become a superpartner of another Hermitian Hamiltonian. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Quantum physics with non-Hermitian operators'.

arXiv:1207.2522•Journal of Physics A Mathematical and Theoretical•Oct 23, 2012•1 citation

Certain properties of Berry's phases in supersymmetric quantum mechanics. II

K M Cheng, P. C. W. Fung

For pt.I see ibid., vol.25, p.1745 (1992). In the first paper the authors studied certain crucial mathematical properties of Abelian Berry's phases in two quantum systems with supersymmetrically related Hamiltonians. They follow up such investigation by extending their analysis to nonAbelian Berry's phases in this present study. They present the derivation of an explicit expression for the difference in the relevant nonAbelian Berry's connections. Also they have derived an expression for a connection one form, which contain the non-Abelian Berry's connection, and which is invariant in the two supersymmetrically related quantum systems. To illustrate their findings mentioned above, they take the example of a Hamiltonian expressible in spin quadrupole. In this example, with a particular choice of supersymmetric partner, they show that the two Berry's connection one forms of the two supersymmetrically related systems may be related by gauge transformation.

Journal of Physics A Mathematical and General•Aug 21, 1992•1 citation

Semi-unitary Transformation Induced Supersymmetric Partner Hulthen System

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

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.

Chinese Physics Letters•Jul 1, 1996•0 citations

Introducing supersymmetric quantum mechanics via point canonical transformations

Gabriel González

Abstract We propose an alternative way to introduce supersymmetric quantum mechanics to physics students using a point canonical coordinate transformation. We provide two point canonical transformations that allow us to obtain new supersymmetric partner Hamiltonians with iso-spectral and non-iso-spectral energy eigenvalues starting from a known solvable Hamiltonian. We illustrate this new approach by applying it to the harmonic oscillator potential.

European Journal of Physics•Mar 11, 2020•0 citations
It is shown that in supersymmetric quantum mechanics the superpartner Hamiltonian H+{\mathit{H}}_{+}H+​ is related to the Hamiltonian H\ensuremath−{\mathit{H}}_{\mathrm{\ensuremath{-}}}H\ensuremath−​ by a semiunitary transformation. The properties of the semiunitary transformation are discussed. \textcopyright{} 1996 The American Physical Society.
The study of the non-Hermitian Hamiltonian systems within the framework of Supersymmetric Quantum mechanics (SUSY QM) has been carried out in literature in the last decade. Most of these potentials are either PT Symmetric or quasi-Hermitian in nature. But no formulation is advanced in literature to the study of general complex potentials within its framework. In this paper, using the complex phase space approach, we carry out the complexification of Supersymmetric Quantum Mechanics to enable the study of any general non-Hermitian Hamiltonian system within its framework. The commutation relations among its operators are enumerated and the underlying symmetry is discussed. The eigenvalues and eigenfunctions of the real and imaginary parts of superpartner Hamiltonians are also investigated.
Being chosen as a differential operator of a special form, the metric η operator has become unitary equivalent to a one-dimensional Hermitian Hamiltonian with a natural supersymmetric structure. We show that fixing the superpartner of this Hamiltonian permits us to determine both the metric operator and the corresponding non-Hermitian Hamiltonian. Moreover, under an additional restriction on the non-Hermitian Hamiltonian, it has become a superpartner of another Hermitian Hamiltonian. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Quantum physics with non-Hermitian operators'.
For pt.I see ibid., vol.25, p.1745 (1992). In the first paper the authors studied certain crucial mathematical properties of Abelian Berry's phases in two quantum systems with supersymmetrically related Hamiltonians. They follow up such investigation by extending their analysis to nonAbelian Berry's phases in this present study. They present the derivation of an explicit expression for the difference in the relevant nonAbelian Berry's connections. Also they have derived an expression for a connection one form, which contain the non-Abelian Berry's connection, and which is invariant in the two supersymmetrically related quantum systems. To illustrate their findings mentioned above, they take the example of a Hamiltonian expressible in spin quadrupole. In this example, with a particular choice of supersymmetric partner, they show that the two Berry's connection one forms of the two supersymmetrically related systems may be related by gauge transformation.