Editing Configuration space (physics) (section)

== Quantum state space ==
{{See also|Projective Hilbert space|Wigner's theorem}}
In [[quantum mechanics]], configuration space can be used (see for example the [[Mott problem]]), but the classical mechanics extension to phase space cannot. Instead, a rather different set of formalisms and notation are used in the analogous concept called [[quantum state space]]. The analog of a "point particle" becomes a single point in <math>\mathbb{C}\mathbf{P}^1</math>, the [[complex projective line]], also known as the [[Bloch sphere]]. It is complex, because a quantum-mechanical [[wave function]] has a complex phase; it is projective because the wave-function is normalized to unit probability.  That is, given a wave-function <math>\psi</math> one is free to normalize it by the total probability <math display="inline">\int\psi^*\psi</math>, thus making it projective.