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.
Bagarello, F., Inoue, A., Trapani, C. (2014). Non-self-adjoint hamiltonians defined by Riesz bases. JOURNAL OF MATHEMATICAL PHYSICS, 55(3) [10.1063/1.4866779].
Non-self-adjoint hamiltonians defined by Riesz bases
BAGARELLO, Fabio;TRAPANI, Camillo
2014-01-01
Abstract
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.
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