Time-Dependent and/or Nonlocal Representations of Hilbert Spaces in Quantum Theory

M. Znojil


A few recent innovations of the applicability of standard textbook Quantum Theory are reviewed. The three-Hilbert-space formulation of the theory (known from the interacting boson models in nuclear physics) is discussed in its slightly broadened four-Hilbert-space update. Among applications involving several new scattering and bound-state problems the central role is played by models using apparently non-Hermitian (often called “crypto-Hermitian”) Hamiltonians with real spectra. The formalism (originally inspired by the topical need for a mathematically consistent description of tobogganic quantum models) is shown to admit even certain unusual nonlocal and/or “moving-frame” representations H(S) of the standard physical Hilbert space of wave functions.


Quantum Theory; cryptohermitian operators of observables; stable bound states; unitary scattering; quantum toboggans; supersymmetry; time-dependent models.

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague