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Biorthogonal quantum mechanics

Brody, Dorje C

Journal of physics. A, Mathematical and theoretical, 2014-01, Vol.47 (3), p.35305-21 [Periódico revisado por pares]

IOP Publishing

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  • Título:
    Biorthogonal quantum mechanics
  • Autor: Brody, Dorje C
  • Assuntos: biorthogonal basis ; Dynamical systems ; Dynamics ; Eigenvalues ; Mathematical analysis ; non-Hermitian Hamiltonian ; Operators ; Orthogonality ; Perturbation methods ; PT symmetry ; Quantum mechanics ; Quantum theory
  • É parte de: Journal of physics. A, Mathematical and theoretical, 2014-01, Vol.47 (3), p.35305-21
  • Notas: ObjectType-Article-1
    SourceType-Scholarly Journals-1
    ObjectType-Feature-2
    content type line 23
  • Descrição: The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called 'biorthogonal quantum mechanics', is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems.
  • Editor: IOP Publishing
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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