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Operator Domains and SUSY Breaking in a Model of SUSYQM with a Singular Potential

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Spectral Analysis of Quantum Hamiltonians

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 224))

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Abstract

The self-adjoint extension of the symmetric supercharges and Hamiltonian of a model of Supersymmetric Quantum Mechanics on the half-line, for the case of a singular superpotential, is analyzed.Th e compatibility of the domains of definition of the different operators and the possibility of effectively implement the graded superalgebra in a dense subspace of the Hilbert space is considered.As a consequence, conditions for SUSY breaking in this model are established.

Mathematics Subject Classification (2010). 81Q10, 34L40, 35A20, 34L05.

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Authors and Affiliations

  1. IFLP – CONICET Deptartamento de Física, Fac. de Ciencias Exactas, UNLP, C.C. 67, 1900, La Plata, Argentina

    H. Falomir & P. A. G. Pisani

Authors
  1. H. Falomir
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  2. P. A. G. Pisani
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Corresponding author

Correspondence to H. Falomir .

Editor information

Editors and Affiliations

  1. , Departamento de Física, P. Universidad Católica de Chile, Santiago, 22, Chile

    Rafael Benguria

  2. , Departamento de Matemáticas, Universidad de Chile, Las Palmeras, Nuñoa 3425, Santiago, Chile

    Eduardo Friedman

  3. , Departamento de Matemática, Universidad de Chile, Las Palmeras, Nuñoa 3425, Santiago, Chile

    Marius Mantoiu

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Falomir, H., Pisani, P.A.G. (2012). Operator Domains and SUSY Breaking in a Model of SUSYQM with a Singular Potential. In: Benguria, R., Friedman, E., Mantoiu, M. (eds) Spectral Analysis of Quantum Hamiltonians. Operator Theory: Advances and Applications, vol 224. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0414-1_7

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