J-selfadjoint operators with C-symmetries: extension theory approach
J-selfadjoint operators with C-symmetries: extension theory approach
Albeverio, S.; Günther, U.; Kuzhel, S.
A well known tool in conventional (von Neumann) quantum mechanics is the selfadjoint extension technique for symmetric operators. It is used, e.g., for the construction of Dirac-Hermitian Hamiltonians with point-interaction potentials. Here we reshape this technique to allow for the construction of pseudo-Hermitian (J-selfadjoint) Hamiltonians with complex point-interactions. We demonstrate that the resulting Hamiltonians are bijectively related with so called hypermaximal neutral subspaces of the defect Krein space of the symmetric operator. This symmetric operator is allowed to have arbitrary but equal deficiency indices
Keywords: PT-symmetric quantum mechanics; pseudo-Hermitian operators; Krein space; extension theory; point interactions; hypermaximal neutral subspace; C-operator; super-symmetry; contraction mapping; resolvent; defect index; defect subspace; extension center
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Journal of Physics A 42(2009), 105205
DOI: 10.1088/1751-8113/42/10/105205
ISSN: 1751-8121
Cited 25 times in Scopus
Permalink: https://www.hzdr.de/publications/Publ-11882