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Non-self-adjoint hamiltonians defined by Riesz bases

Atsushi InoueFabio BagarelloCamillo Trapani

subject

Pure mathematicsQuantum PhysicsHamiltonian operatorBasis (linear algebra)Spectrum (functional analysis)Hilbert spaceFOS: Physical sciencesStatistical and Nonlinear PhysicsRiesz basesMathematical Physics (math-ph)symbols.namesakeSettore MAT/05 - Analisi MatematicaSimple (abstract algebra)symbolsQuantum Physics (quant-ph)Settore MAT/07 - Fisica MatematicaSelf-adjoint operatorEigenvalues and eigenvectorsMathematical PhysicsMathematics

description

We discuss some features of non-self-adjoint Hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a Riesz basis of Hilbert space. Among other things, {we give conditions under which these Hamiltonians} can be factorized in terms of generalized lowering and raising operators.

yearjournalcountryeditionlanguage
2014-01-01
10.1063/1.4866779http://arxiv.org/abs/1402.6199