11,876 research outputs found

    SUSUSY quantum mechanics

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    The exactly solvable eigenproblems in Schr\"odinger quantum mechanics typically involve the differential "shift operators". In the standard supersymmetric (SUSY) case, the shift operator turns out to be of first order. In this work, I discuss a technique to generate exactly solvable eigenproblems by using second order shift operators. The links between this method and SUSY are analysed. As an example, we show the existence of a two-parametric family of exactly solvable Hamiltonians, which contains the Abraham-Moses potentials as a particular case.Comment: 7 pages, 2 encapsulated postscript figures, uses epsf.sty talk given at the II International Workshop on Classical and Quantum Integrable Systems, Dubna (Russia), 8-12 July (1996) to be published in Int. J. Mod. Phys.

    Supersymmetric Quantum Mechanics

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    Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulas concerning SUSY QM of first and second order for one-dimensional arbitrary systems, and we will illustrate the method through the trigonometric Poschl-Teller potentials. Some intrinsically related subjects, as the algebraic structure inherited by the new Hamiltonians and the corresponding coherent states will be analyzed. The technique will be as well implemented for periodic potentials, for which the corresponding spectrum is composed of allowed bands separated by energy gaps.Comment: 36 pages, 8 figures, lectures delivered at the Advanced Summer School 2009, Cinvestav (Mexico City), July 200

    Higher-order supersymmetric quantum mechanics

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    We review the higher-order supersymmetric quantum mechanics (H-SUSY QM), which involves differential intertwining operators of order greater than one. The iterations of first-order SUSY transformations are used to derive in a simple way the higher-order case. The second order technique is addressed directly, and through this approach unexpected possibilities for designing spectra are uncovered. The formalism is applied to the harmonic oscillator: the corresponding H-SUSY partner Hamiltonians are ruled by polynomial Heisenberg algebras which allow a straight construction of the coherent states.Comment: 42 pages, 12 eps figure

    Complex solutions to Painleve IV equation through supersymmetric quantum mechanics

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    In this work, supersymmetric quantum mechanics will be used to obtain complex solutions to Painleve IV equation with real parameters. We will also focus on the properties of the associated Hamiltonians, i.e. the algebraic structure, the eigenfunctions and the energy spectra.Comment: 5 pages, 3 figures. Talk given at the Advanced Summer School 2011, Cinvestav (Mexico City), July 201
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