First sentence: The arena for quantum mechanics of an N particle system in a d-dimensional Euclidean space is the Hilbert space H = L2((Rd)N), (1.1) whose unit vectors (i.e. vectors of length 1) (x1, ..., xN) (called wave functions) describe states of the system, (x1, ..., xN) 2 being interpreted as the probability density (with respect to the Lebesgue measure) for the N particles at positions x1, ..., xN in Rd. /