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

Canadian Journal of Physics

Noncompact orthosympletic supersymmetry: an example from N = 1, d = 1 supersymmetric quantum mechanics

H. A. Schmitt, A. Mufti

Published Dec 1, 1990• 2 citations
Publisher

Abstract

The supersymmetric quantum mechanical harmonic oscillator, a particular example of an N = 1, d = 1 supersymmetric quantum mechanical model, is used to construct a Hamiltonian exhibiting a noncompact orthosymplectic supersymmetry. This Hamiltonian is the strong-coupling limit of the Jaynes–Cummings model.
DOI
10.1139/p90-208

Related papers

Two-level Jaynes-Cummings Hamiltonian as a supersymmetric quantum-mechanical system

H. A. Schmitt, A. Mufti

Using a realization of the noncompact orthosymplectic superalgebra $\mathrm{Osp}(\frac{2}{2}, R)$, the two-level Jaynes-Cummings Hamiltonian is shown to be a supersymmetric quantum-mechanical system in the sense of Witten. The existence of the supersymmetry is shown to place a restriction on the physical parameters of the Hamiltonian.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Apr 15, 1991•8 citations

Supersymmetry in the Jaynes-Cummings model

Octavio Castaños

A review is presented of the Darboux method and its relation to the supersymmetric quantum mechanics, together with the embedding of a n-dimensional scalar Hamiltonian into a supersymmetric matrix. It is also shown that the Jaynes-Cummings model, with or without rotating wave approximation, admit a supersymmetric quantum mechanics description.

AIP conference proceedings•Jan 1, 2013•2 citations

A Study about the Supersymmetry in the context of Quantum Mechanics

Marques, Fabricio

In this work we present an introduction to Supersymmetry in the context of 1-dimensional Quantum Mechanics. For that purpose we develop the concept of hamiltonians factorization using the simple harmonic oscillator as an example, we introduce the supersymmetric oscilator and, next, we generalize these concepts to introduce the fundamentals of Supersymmetric Quantum Mechanics. We also discuss useful tools to solve problems in Quantum Mechanics which are intrinsecally related to Supersymmetry as hierarchy of hamiltonians and shape invariance. We present two approximation methods which will be specially useful: the well known Variational Method and the Logarithmic Perturbation Theory, the latter being closely related to the concepts of superpotentials and hierarchy of hamiltonians. Finally, we present problems related to superpotentials which are monomials in even powers of the x coordinate multiplied by the sign function epsilon(x), which seems to be a new class of problems in Supersymmetric Quantum Mechanics.

arXiv:1111.0827•Nov 3, 2011•1 citation

Non-Hermitian inverted harmonic oscillator-type Hamiltonians generated from supersymmetry with reflections

R. D. Mota, D. Ojeda-Guillén, M. Salazar–Ramírez +1 more

By modifying and generalizing known supersymmetric models, we are able to find four different sets of one-dimensional Hamiltonians for the inverted harmonic oscillator. The first set of Hamiltonians is derived by extending the supersymmetric quantum mechanics with reflections to non-Hermitian supercharges. The second set is obtained by generalizing the supersymmetric quantum mechanics valid for non-Hermitian supercharges with the Dunkl derivative instead of [Formula: see text]. Also, by changing the derivative [Formula: see text] by the Dunkl derivative in the creation and annihilation-type operators of the standard inverted harmonic oscillator [Formula: see text], we generate the third set of Hamiltonians. The fourth set of Hamiltonians emerges by allowing a parameter of the supersymmetric two-body Calogero-type model to take imaginary values. The eigensolutions of definite parity for each set of Hamiltonians are given.

arXiv:1707.09082•Modern Physics Letters A•Jan 16, 2019•5 citations

Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations

C Quesne

A harmonic oscillator Hamiltonian augmented by a non-Hermitian -symmetric part and its su(1,1) generalizations, for which a family of positive-definite metric operators was recently constructed, are re-examined in a supersymmetric context. Some quasi-Hermitian supersymmetric extensions of such Hamiltonians are proposed by enlarging su(1,1) to a superalgebra. This allows the construction of new non-Hermitian Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.

arXiv:0710.2453•Journal of Physics A Mathematical and Theoretical•Jun 3, 2008•12 citations

Recent Developments in Supersymmetric Quantum Mechanics

Georg Junker

Some recent results in supersymmetric quantum mechanics are presented. New semi-classical approximation formulas for Witten's realization of supersymmetric quantum mechanics are discussed. Implications of the supersymmetric structure of Pauli's Hamiltonian are also considered. In particular, the paramagnetisation of a non-interacting electron gas is related to a modified version of Witten's index. We also show that the supersymmetry in this system provides a new counter example for the paramagnetic conjecture.

arXiv:cond-mat/9403088•Mar 29, 1994•0 citations
Using a realization of the noncompact orthosymplectic superalgebra Osp(22,R)\mathrm{Osp}(\frac{2}{2}, R)Osp(22​,R), the two-level Jaynes-Cummings Hamiltonian is shown to be a supersymmetric quantum-mechanical system in the sense of Witten. The existence of the supersymmetry is shown to place a restriction on the physical parameters of the Hamiltonian.
In this work we present an introduction to Supersymmetry in the context of 1-dimensional Quantum Mechanics. For that purpose we develop the concept of hamiltonians factorization using the simple harmonic oscillator as an example, we introduce the supersymmetric oscilator and, next, we generalize these concepts to introduce the fundamentals of Supersymmetric Quantum Mechanics. We also discuss useful tools to solve problems in Quantum Mechanics which are intrinsecally related to Supersymmetry as hierarchy of hamiltonians and shape invariance. We present two approximation methods which will be specially useful: the well known Variational Method and the Logarithmic Perturbation Theory, the latter being closely related to the concepts of superpotentials and hierarchy of hamiltonians. Finally, we present problems related to superpotentials which are monomials in even powers of the x coordinate multiplied by the sign function epsilon(x), which seems to be a new class of problems in Supersymmetric Quantum Mechanics.
By modifying and generalizing known supersymmetric models, we are able to find four different sets of one-dimensional Hamiltonians for the inverted harmonic oscillator. The first set of Hamiltonians is derived by extending the supersymmetric quantum mechanics with reflections to non-Hermitian supercharges. The second set is obtained by generalizing the supersymmetric quantum mechanics valid for non-Hermitian supercharges with the Dunkl derivative instead of [Formula: see text]. Also, by changing the derivative [Formula: see text] by the Dunkl derivative in the creation and annihilation-type operators of the standard inverted harmonic oscillator [Formula: see text], we generate the third set of Hamiltonians. The fourth set of Hamiltonians emerges by allowing a parameter of the supersymmetric two-body Calogero-type model to take imaginary values. The eigensolutions of definite parity for each set of Hamiltonians are given.
Some recent results in supersymmetric quantum mechanics are presented. New semi-classical approximation formulas for Witten's realization of supersymmetric quantum mechanics are discussed. Implications of the supersymmetric structure of Pauli's Hamiltonian are also considered. In particular, the paramagnetisation of a non-interacting electron gas is related to a modified version of Witten's index. We also show that the supersymmetry in this system provides a new counter example for the paramagnetic conjecture.