ok, again, just like the higgs feild thread i need a nice simple explaination of hilbert space, cheers. PS try not to use to much stuff about vectors they lose me right now although im starting to understand.

hilbert space. well it will be hard to explain what a hilbert space without referring to stuff like vector spaces. so i won t.

a hilbert space is a complete inner product space. that is, a vector space, which is equipped with an inner product (like the dot product in R3). an inner product is just a rule for taking two vectors, multiplying them, and getting a number out. the space must also satisfy the condition that if an infinite series of vectors in the space exists that looks like it wants to converge, then it must converge to something in the space. this is called completeness.

Lethe's explanation is excellent. The reason Hilbert spaces are important is that they are the most general structure to have all the topological and algebraic properties of finite dimensional vector spaces. In particular, to generalize "Fourier Transforms" you need a Hilber Space.

If you don't know about vectors, then I'm confused: Where did you ever hear about Hilbert space? Perhaps if you give us the context of your encounter with Hilbert space, then we may construct an explanation better suited to your understanding.

well im kinda learning qauntum mechanics in patches, i found it so interesting that i started just looking it up all over the net, i come accross a lot of words which i research and find a whole new concept and i really havent learnt the basics like vectors and this kind of terminology to understand it all. If anyone can suggest a good guide to QM on the net, like one that goes through each aspect in order i would be very gratefull if they could post a link here, thnx

If you're plain interrested and have plenty of time you could just surf the web of some University. Look for a course outline and get the books they're reading.