Quasi-hermiticity and the Role of a Metric in Some Boson Hamiltonians

Author： Geyer Hendrik B.   Scholtz Frederik G.   Snyman Izak  

Publisher： Springer Publishing Company

ISSN： 0011-4626

Source： Czechoslovak Journal of Physics, Vol.54, Iss.10, 2004-10, pp. : 1069-1073

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Abstract

The strategy of endowing PT-symmetric quantum mechanics with a positive definite metric, by adopting a modified inner product, has recently been explored in a simple non-hermitian quadratic boson Hamiltonian. We reconsider this analysis with emphasis on the question of a unique metric linked to the identification of an irreducible set of observables. Our results emphasise the necessity to ensure such a unique metric in order to establish a viable quantum mechanical framework.

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