# Deformation in supersymmetric quantum mechanics

TL;DR: In this article, a comprehensive scheme of quantum deformation is presented and applied to supersymmetric quantum mechanics, and the connection with a recently proposed model and explore a new mode of quantum DEformation is explored.

Abstract: We present a comprehensive scheme of deformation and apply it to supersymmetric quantum mechanics. We work out the connection with a recently proposed model and explore a new mode of quantum deformation.

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TL;DR: In this article, general conditions for dynamical supersymmetry breaking are discussed and examples are given (in 0 + 1 and 2 + 1 dimensions) in which such a program in four dimensions is possible.

Abstract: General conditions for dynamical supersymmetry breaking are discussed. Very small effects that would usually be ignored, such as instantons of a grand unified theory, might break supersymmetry at a low energy scale. Examples are given (in 0 + 1 and 2 + 1 dimensions) in which dynamical supersymmetry breaking occurs. Difficulties that confront such a program in four dimensions are described.

3,164 citations

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TL;DR: The quantum group SU(2)q is discussed in this paper by a method analogous to that used by Schwinger to develop the quantum theory of angular momentum such theory of the q-analogue of the quantum harmonic oscillator, as is required for this purpose.

Abstract: The quantum group SU(2)q is discussed by a method analogous to that used by Schwinger to develop the quantum theory of angular momentum Such theory of the q-analogue of the quantum harmonic oscillator, as is required for this purpose, is developed

1,510 citations

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Duke University

^{1}TL;DR: In this article, a new realisation of the quantum group SUq(2) is constructed by means of a q-analogue to the Jordan-Schwinger mapping, determining thereby both the complete representation structure and qanalogues to the Wigner and Racah operators.

Abstract: A new realisation of the quantum group SUq(2) is constructed by means of a q-analogue to the Jordan-Schwinger mapping, determining thereby both the complete representation structure and q-analogues to the Wigner and Racah operators. To achieve this realisation, a new elementary object is defined, a q-analogue to the harmonic oscillator. The uncertainty relation for position and momentum in a q-harmonic oscillator is quite unusual.

1,366 citations

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TL;DR: In this article, the Schrodinger equation for the one-dimensional harmonic oscillator was considered, with the normal derivative replaced by a q-derivative, and normalizable solutions were found and the q-generalization of the Hermite polynomials was given.

Abstract: We consider the Schrodinger equation for the one-dimensional harmonic oscillator, but with the normal derivative replaced by a q-derivative. The normalizable solutions are found and the q-generalization of the Hermite polynomials is given. The free equation is also considered, but no normalizable eigenstates exist even if the system is in a box.

159 citations

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TL;DR: In this paper, a pedagogical review on supersymmetry in quantum mechanis is presented which provides a comprehensive coverage of the subject and the key ingredients on the quantization of the systems with anticommuting variables are discussed.

Abstract: A pedagogical review on supersymmetry in quantum mechanis is presented which provides a comprehensive coverage of the subject. First, the key ingredients on the quantization of the systems with anticommuting variables are discussed. The supersymmetric Hamiltotian in quantum mechanics is then constructed by emphasizing the role of partner potentials and the superpotentials. We also make explicit the mathematical formulation of the Hamiltonian by considering in detail the N=1 and N=2 supersymmetric (quantum) mechanics. Supersymmetry is then discussed in the context of one-dimensional problems and the importance of the factorization method is highlighted. We treat in detail the technique of constructing a hierarchy of Hamiltonians employing the so-called ‘shape-invariance’ of potentials. To make transparent the relationship between supersymmetry and solvable potentials, we also solve several examples. We then go over to the formulation of supersymmetry in radial problems, paying a special attention to the Co...

128 citations

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