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I hate to be 'that guy', but I've heard so-called "Hilbert Space" referenced many times. I can imagine that it's derived from physicist David Hilbert. I'd guess that you'd learn about it in an Undergrad course.
dextercioby said:he's a mathematician, just like Weyl and von Neumann.
I figured that I'd get a better answer from this website, what with it being solely dedicated to physics, and being primarily filled with physics professors and students.A. Neumaier said:You should have guessed that definitions can be looked up in many places, for example in wikipedia. Please do your work before asking others to work for you.
So which prior efforts did you make after my suggestion? Nothing is obtained for free, and nobody here likes to repeat stuff that you can read in many places.RafiG709 said:I figured that I'd get a better answer from this website, what with it being solely dedicated to physics, and being primarily filled with physics professors and students.
Good to know, I'll do my research first beforehand, next time. Thanks for the advice.A. Neumaier said:So which prior efforts did you make after my suggestion? Nothing is obtained for free, and nobody here likes to repeat stuff that you can read in many places.
On standard mathematics, wikipedia is quite good and far more thorough for a first orientation than anything you'd be explained here - just remain aware that nothing you read (whether on wikipedia or here) is guaranteed to be correct. You must do your own checking anyway.
Then when you have questions that wikipedia leaves open, or when you get inconsistent messages from different sources, its the time to come here to PF and ask. (About Hilbert spaces in the math section, about the underlying physics in the present one.)
Strange. What do you think makes a person a physicist? Are a paper ''The foundations of physics'' where general relativity was derived from an action principle, and a 2-volume treatise on ''Methods of mathematical physics" not enough? Many with a Ph.D. in physics (and thus certified physicists) don't even achieve that much.dextercioby said:I wouldn't call Hilbert a physicist, he's a mathematician
Dirac defined what bras and kets are. They need not be in the Hilbert space - this accounts for part of their usefulness.radium said:The physicist answer would be a complex vector space which is self dual and is endowed with an inner product between vectors and dual vectors. In quantum mechanics these would be kets (vector) and bras (dual vector). A ket is the complex conjugate of a bra etc.
A. Neumaier said:Strange. What do you think makes a person a physicist? Are a paper ''The foundations of physics'' where general relativity was derived from an action principle, and a 2-volume treatise on ''Methods of mathematical physics" not enough. Many with a Ph.D. in physics (and thus certified physicists) don't even achieve that much.
Sure, and a person contributing significantly to physics is a physicist. What else should make a person a physicist?martinbn said:A mathematician can contribute to physics.
A. Neumaier said:Sure, and a person contributing significantly to physics is a physicist. What else should make a person a physicist?
Why should a person be only one thing? This is very unnatural!martinbn said:there are plenty of examples of mathematicians contributing significantly to physics (Newton one of them), but they are still mathematicians. Why would they be anything else?!
Hilbert Space is a mathematical concept that refers to a complete and infinite-dimensional vector space, often used in physics and engineering to describe the behavior of systems with infinitely many degrees of freedom.
The main characteristics of Hilbert Space include being a complete vector space, having a finite or infinite number of dimensions, and being equipped with an inner product that allows for the definition of length and angle.
Hilbert Space differs from other vector spaces in that it is complete, meaning that it contains all possible limits of convergent sequences, and it has an inner product that allows for the definition of length and angle between vectors.
Hilbert Space has many practical applications in physics and engineering, including quantum mechanics, signal processing, and control theory. It is also used in functional analysis and harmonic analysis.
No, Hilbert Space is not a physical space in the traditional sense. It is a mathematical concept that is used to describe and analyze systems with infinitely many degrees of freedom, such as wave functions in quantum mechanics.