  In orthodox quantum mechanics, normalized vectors in Hilbert spaces represent states of physical systems. When the Hilbert space is of infinite dimension, state vectors can be represented by functions, the so-called ‘wave functions.’ In any given basis, there is a unique wave function that corresponds to the state vector in that basis. (For an entry level review of the highlights of the mathematical formalism and the basic principles of quantum mechanics, see the entry on quantum mechanics, Albert 1992, Hughes 1989, Part I, and references therein; for more advanced reviews, see Bohm 1951 and Redhead 1987, chapters 1-2 and the mathematical appendix.)