quality:corruption
Probability interpretation

For the general case of N particles with spin in 3d, if Ψ is interpreted as a probability amplitude, the probability density is ρ (r 1 ⋯ r N, s z 1 ⋯ s z N, t) = | Ψ (r 1 ⋯ r N, s z 1 ⋯ s z N, t) | 2 {\displaystyle \rho \left(\mathbf {r} _{1}\cdots \mathbf {r} _{N},s_{z\,1}\cdots s_{z\,N},t\right)=\left|\Psi \left(\mathbf {r} _{1}\cdots \mathbf {r} _{N},s_{z\,1}\cdots s_{z\,N},t\right)\right|^{2}}

and the probability that particle 1 is in region R with spin s = m and particle 2 is in region R with spin s = m etc. at time t is the integral of the probability density over these regions and evaluated at these spin numbers: