Wave function

"… what is the wave function? Is it a complete and comprehensive representation of the world? Or do we need additional physical quantities to fully capture reality, as Albert Einstein and others suspected? Or does the wave function have no direct connection with reality at all, merely characterizing our personal ignorance about what we will eventually measure in our experiments? Until s definitively answer these questions, they can’t really be said to understand quantum mechanics — thus Feynman’s lament. Which is bad, because quantum mechanics is the most fundamental theory we have, sitting squarely at the center of every serious attempt to formulate deep laws of nature. If nobody understands quantum mechanics, nobody understands the universe."

"What is the empirical content of quantum mechanics? Or how does the wave function assigned to a relate to the results of measurements on the system? The well-known connection rule is the , which has been precisely tested by experiments. It says that a (projective) measurement of an A on a system with the wave function |ψ⟩ will randomly obtain one of the of A, and the probability of obtaining an eigenvalue ai is given by |⟨ai|ψ⟩|2, where |ai⟩ is the corresponding to the eigenvalue ai."

"... was formalized by a number of authors ... as the requirement that the wave function of a multi-electron system is in the coordinates, and , of all the electrons. This principle was incorporated into statistical mechanics by Enrico Fermi ... and Dirac, ... and for this reason particles obeying the exclusion principle are generally called 's,' just as particles like photons for which the wave function is symmetric and which obey the statistics of Bose and Einstein are called 's.'"