Non-self-adjoint Hamiltonians with complex eigenvalues

Fabio Bagarello, Bagarello

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Motivated by what one observes dealing with PT-symmetric quantum mechanics, we discuss what happens if a physical system is driven by a diagonalizable Hamiltonian with not all real eigenvalues. In particular, we consider the functional structure related to systems living in finite-dimensional Hilbert spaces, and we show that certain intertwining relations can be deduced also in this case if we introduce suitable antilinear operators. We also analyze a simple model, computing the transition probabilities in the broken and in the unbroken regime.
Original languageEnglish
Number of pages17
JournalJOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL
Volume49
Publication statusPublished - 2016

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Hamiltonians
Living Systems
Quantum theory
Hilbert spaces
Hilbert space
Transition Probability
transition probabilities
Quantum Mechanics
quantum mechanics
eigenvalues
Eigenvalue
operators
Computing
Operator
Model

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Non-self-adjoint Hamiltonians with complex eigenvalues. / Bagarello, Fabio; Bagarello.

In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, Vol. 49, 2016.

Research output: Contribution to journalArticle

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