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States in the Hilbert space formulation and the phase space formulation of quantum mechanics (1210.7672v1)
Published 29 Oct 2012 in math-ph, math.MP, and quant-ph
Abstract: W consider the problem of testing if a given matrix in the Hilbert space formulation of quantum mechanics or a function in the phase space formulation of quantum theory represent a quantum state. We propose several practical criteria to recognise states in these both versions of quantum physics. After minor modifications they can be applied to check positivity of any operators acting in a Hilbert space or positivity of any functions from an algebra with a Weyl type * -- product.
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