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Quantum Bi-Hamiltonian systems, alternative Hermitian structuresand Bi-Unitary transformations


Abstract


We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space.We give a necessary and sufficient condition so that the Hermitian structures are in generic position. Finally the transformations of the bi-unitary group are explicitly obtained.

DOI Code: 10.1285/i15900932v23n2p173

Keywords: Functional analysis; Quantum mechanics; Symplectic geometry; Spectral theory

Classification: 37K05; 58D19

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