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Qmechanic ♦
Qmechanic ♦
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The Weyl-Wigner representationWeyl-Wigner representation is a useful tool to study QM from a semiclassical, phase-space point of view. My question is simple: if this method is so close to classical mechanics, why don't we use it for the whole theory of QM? Why do we need Hilbert spaces?

The Weyl-Wigner representation is a useful tool to study QM from a semiclassical, phase-space point of view. My question is simple: if this method is so close to classical mechanics, why don't we use it for the whole theory of QM? Why do we need Hilbert spaces?

The Weyl-Wigner representation is a useful tool to study QM from a semiclassical, phase-space point of view. My question is simple: if this method is so close to classical mechanics, why don't we use it for the whole theory of QM? Why do we need Hilbert spaces?

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Mauro Giliberti
Mauro Giliberti
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What is wrong with Weyl-Wigner representation?

The Weyl-Wigner representation is a useful tool to study QM from a semiclassical, phase-space point of view. My question is simple: if this method is so close to classical mechanics, why don't we use it for the whole theory of QM? Why do we need Hilbert spaces?