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Or is it only theoretical.
Hilbert space is a mathematical concept. It exists the same way that sets exist, or vectors, or the number line.KarminValso1724 said:Or is it only theoretical.
Hilbert space is a purely mathematical concept, generalized Euclidean space. Much of quantum theory uses Hilbert space as part of the development.FactChecker said:There are a great many examples of Hilbert spaces. They do exist. You might want to ask if a particular space you are interested in is a Hilbert space.
Yes. Hilbert spaces are more the rule than the exception in spaces that we study. There are examples everywhere. The only reasonable question is whether a particular unusual space is a Hilbert space. So the OP should specify what space he is asking about.mathman said:Hilbert space is a purely mathematical concept, generalized Euclidean space. Much of quantum theory uses Hilbert space as part of the development.
The real numbers and the complex plane are both Hilbert spaces.KarminValso1724 said:Or is it only theoretical.
Although it might simply be a matter of definition, but Hilbert space is usually defined as an infinite dimensional analog of n dimensional Euclidean space.Zafa Pi said:The real numbers and the complex plane are both Hilbert spaces.
The opening post asked if a Hilbert Space exist so I gave the simplest ones, and BTW:mathman said:Although it might simply be a matter of definition, but Hilbert space is usually defined as an infinite dimensional analog of n dimensional Euclidean space.