States in the Hilbert space formulation and in the phase space formulation of quantum mechanics |
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Authors: | J Tosiek P Brzykcy |
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Institution: | Institute of Physics, Technical University of ?ód?, Wólczańska 219, 90-924 ?ód?, Poland |
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Abstract: | We consider the problem of testing whether a given matrix in the Hilbert space formulation of quantum mechanics or a function considered in the phase space formulation of quantum theory represents a quantum state. We propose several practical criteria for recognising states in these two 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 ∗-product of Weyl type. |
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Keywords: | Deformation quantisation Wigner function Density operator |
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