Supersymmetric Quantum Mechanics and Solvable Models

Bougie, Jonathan; Gangopadhyaya, Asim; Mallow, Jeffry V.; Rasinariu, Constantin

doi:10.3390/sym4030452

Cited by 40 publications

(64 citation statements)

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“…Since the aforementioned zero modes play a crucial role towards the formulation of the quantum theory of supersymmetric Chern-Simons vortices, in this paper we shall present an interesting property of the zero modes of models with global N = 2 spacetime supersymmetry. Particularly, we find that the zero modes of fermionic and bosonic fluctuations of Abelian gauge models having a global N = 2 spacetime supersymmetry in (2 + 1)-dimensions, can separately constitute two N = 2, d = 1 supersymmetric quantum algebras [15][16][17][18][19][20][21][22], with the zero modes being the corresponding quantum Hilbert space vectors. Moreover, due to the N = 2 global spacetime supersymmetry of the theory, the underlying one dimensional N = 2 supersymmetric quantum algebras can form a centrally extended N = 4, d = 1 supersymmetric quantum algebra.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric Chern–Simons vortex systems and extended supersymmetric quantum mechanics algebras

Oikonomou

2013

Nuclear Physics B

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We study N = 2 supersymmetric Chern-Simons Higgs models in (2+1)-dimensions and the existence of extended underlying supersymmetric quantum mechanics algebras. Our findings indicate that the fermionic zero modes quantum system in conjunction with the system of zero modes corresponding to bosonic fluctuations, are related to an N = 4 extended 1-dimensional supersymmetric algebra with central charge, a result closely connected to the N = 2 spacetime supersymmetry of the total system. We also add soft supersymmetric terms to the fermionic sector in order to examine how this affects the index of the corresponding Dirac operator, with the latter characterizing the degeneracy of the solitonic solutions. In addition, we analyze the impact of the underlying supersymmetric quantum algebras to the zero mode bosonic fluctuations. This is relevant to the quantum theory of self-dual vortices and particularly for the symmetries of the metric of the space of vortices solutions and also for the non-zero mode states of bosonic fluctuations.

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Section: Introductionmentioning

confidence: 99%

Supersymmetric Chern–Simons vortex systems and extended supersymmetric quantum mechanics algebras

Oikonomou

2013

Nuclear Physics B

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“…In Ref. [4,5], the authors showed that these superpotentials obey an infinite set of PDEs. In this section, we will describe how to generate these shape invariant systems from the PDEs.…”

Section: Shape Invariant Superpotentialsmentioning

confidence: 99%

“…Since Eq. (3) must hold for an arbitrary value of , we can expand the equation in powers of , and require that the coefficient of each power vanishes, leading to the following two independent equations [4,5] :…”

Section: A Conventional Superpotentialsmentioning

confidence: 99%

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Inter-relations between additive shape invariant superpotentials

et al. 2020

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All known additive shape invariant superpotentials in nonrelativistic quantum mechanics belong to one of two categories: superpotentials that do not explicitly depend on , and their -dependent extensions. The former group themselves into two disjoint classes, depending on whether the corresponding Schrödinger equation can be reduced to a hypergeometric equation (type-I) or a confluent hypergeometric equation (type-II). All the superpotentials within each class are connected via point canonical transformations. Previous work [19] showed that type-I superpotentials produce type-II via limiting procedures. In this paper we develop a method to generate a type I superpotential from type II, thus providing a pathway to interconnect all known additive shape invariant superpotentials.

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“…Arai [5] demonstrated a class of supersymmetric quantum mechanics whose eigenvalues problem has a solvable spectrum. Similarly, in a review paper, Bougie et al [6] presented solvable models within the SUSYQM framework. The authors prove that shape of invariance conditions allows to solve analytically many quantum systems.…”

Section: Introductionmentioning

confidence: 96%

Exact solution of the Schrödinger equation with a new expansion of anharmonic potential with the use of the supersymmetric quantum mechanics and factorization method

Mikulski¹,

Konarski

Eder³

et al. 2015

J Math Chem

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The study involves finding exact eigenvalues of the radial Schrödinger equation for new expansion of the anharmonic potential energy function. All analytical calculations employ the mathematical formalism of the supersymmetric quantum mechanics. The novelty of this study is underlined by the fact that for the first time the recurrence formulas for rovibrational bound energy levels have been derived employing factorization method and algebraic approach. The ground state and the excited states have been determined by means of the hierarchy of the isospectral Hamiltonians. The Riccati nonlinear differential equation with superpotentials has been solved analytically. It has been shown that exact solutions exist when the potential and superpotential parameters satisfy certain supersymmetric constraints. The results obtained can be utilized both in computations of quantum chemistry and theoretical spectroscopy of diatomic molecules.

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Supersymmetric Quantum Mechanics and Solvable Models

Cited by 40 publications

References 41 publications

Supersymmetric Chern–Simons vortex systems and extended supersymmetric quantum mechanics algebras

Supersymmetric Chern–Simons vortex systems and extended supersymmetric quantum mechanics algebras

Inter-relations between additive shape invariant superpotentials

Exact solution of the Schrödinger equation with a new expansion of anharmonic potential with the use of the supersymmetric quantum mechanics and factorization method

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