Non-self-adjoint hamiltonians defined by Riesz bases

Journal Article · Sat Mar 15 00:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4866779· OSTI ID:22251135

Bagarello, F., E-mail: [e-mail] ^[1]; Inoue, A., E-mail: [e-mail] ^[2]; Trapani, C., E-mail: [e-mail] ^[3]

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1. Dipartimento di Energia, Ingegneria dell'Informazione e Modelli Matematici, Facoltà di Ingegneria, Università di Palermo, I-90128 Palermo, Italy and INFN, Università di Torino, Torino (Italy)
2. Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180 (Japan)
3. Dipartimento di Matematica e Informatica, Università di Palermo, I-90123 Palermo (Italy)

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.

• OSTI ID: 22251135
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EIGENVECTORS
HAMILTONIANS
HILBERT SPACE