Configuration Space And Hilbert Space For A Physicist Without Knowledge Of Analysis I have passed calculus course, have basic knowledge of complex numbers and passed introductory linear algebra course. I am trying to study Griffith Quantum Mechanics book, but I am also checking some other books simultaneously, I see stuff about Hilbert Space, Configuration Space and other stuff I don't know about. I have not studied any analysis book, is there any appropriate book to get straightly to the intended topics? I mean a book which provides my needs?
 A: The configuration space comprises all the pairs $(\vec r, \vec p)$, where $\vec r$ is the position and $\vec p$ the linear momentum. (In QM one cannot assume that for a given $\vec r $ the particle has to have a precise $\vec p $.) It is also named "phase space".
But in general the configuration space doesn't have to be positions and linear momenta, but some other variables. One can find in the literature the concepts of "generalized coordinates" and generalized momenta. In this case the Hilbert space comprises functions of these variables.
The Hilbert space is the collection of functions defined on some variables, and fulfilling some conditions as for instance integrability in absolute square (see a more rigorous definition in Wikipedia, http://en.wikipedia.org/wiki/Hilbert_space).
A typical example of functions that can be elements of a Hilbert space (if the conditions are fulfilled) are the wave-functions defined on the positions of all the particles in a given system of particles (position representation). (Other representations are possible too, momentum representation if the variables in the function are momenta, or sometimes energy representation, and others).
For belonging to a Hilbert space, a function has to fulfill some conditions, e.g.  form a Hilbert space.
(Book recommended: "Quantum Theory: Concepts and Methods", by Asher Peres, (Kluwer Academic Publishers, 1993). Chapter 4 goes straightly to Hilbert spaces, and explains their properties.)
