In classical mechanics we use a 6n-dimensional phase space, itself a vector space, to describe the state of a given system at any one point in time, with the evolution of the state of a system being described in terms of a trajectory through the corresponding phase space. However, in quantum mechanics we instead use Hilbert spaces. What is the intuitive reasoning for why we use Hilbert spaces? Is it simply due to the non-commutative nature of observables and the fact that we now have operators acting on states to extract observable quantities and also time evolve them, and these operators naturally act on a Hilbert space?(adsbygoogle = window.adsbygoogle || []).push({});

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# I Why are Hilbert spaces used in quantum mechanics?

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