nLab Born rule

Contents

Idea

The Born rule is the core statement of coordination in the foundations of quantum physics:

In its version for pure states the Born rule says that

for $A$ an observable in the form of a Hermitean operator on the given Hilbert space $\mathcal{H}$ of pure quantum states,
$P$ denoting the projection operator on a give eigenstate of this operator,
$\pi \,\in\, \mathcal{H}$ a pure state;

then the probability of observing the given eigenstate in a quantum system which is in state $\psi$ equals

\frac{ \langle \psi \vert P \vert \psi \rangle }{ \langle \psi \vert \psi \rangle }