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Operator domains and SUSY breaking in a model of SUSYQM with a singular potential. (English) Zbl 1270.81102
Benguria, Rafael (ed.) et al., Spectral analysis of quantum Hamiltonians. Spectral Days 2010. Selected papers of the conference, Santiago, Chile, September 2010. Basel: Birkhäuser (ISBN 978-3-0348-0413-4/hbk; 978-3-0348-0414-1/ebook). Operator Theory: Advances and Applications 224, 133-145 (2012).
Summary: 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. The 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.
For the entire collection see [Zbl 1257.00013].

MSC:
81Q60 Supersymmetry and quantum mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
35A20 Analyticity in context of PDEs
34L05 General spectral theory of ordinary differential operators
81R40 Symmetry breaking in quantum theory
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