WebAs mentioned in Definition 3.1, Hilbert spaces can be finite- or infinite-dimensional, as opposed to classical phase spaces (which are always 6n-dimensional, where nis the particle number). We shall therefore investigate those two cases separately. 3.1.1 Finite–Dimensional Hilbert Spaces Web1.1 Hilbert space ⋆ In quantum mechanics the state of a physical system is represented by a vector in a Hilbert space: a complex vector space with an inner product. The term “Hilbert …
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