Editing Wave function (section)

====Probability interpretation====
For the general case of {{mvar|N}} particles with spin in 3d, if {{math|Ψ}} is interpreted as a probability amplitude, the probability density is
<math display="block">\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</math>

and the probability that particle 1 is in region {{math|''R''<sub>1</sub>}} with spin {{math|1=''s''<sub>''z''1</sub> = ''m''<sub>1</sub>}} ''and'' particle 2 is in region {{math|''R''<sub>2</sub>}} with spin {{math|1=''s''<sub>''z''2</sub> = ''m''<sub>2</sub>}} etc. at time {{math|''t''}} is the integral of the probability density over these regions and evaluated at these spin numbers:

:<math>P_{\mathbf{r}_1\in R_1,s_{z\,1} = m_1, \ldots, \mathbf{r}_N\in R_N,s_{z\,N} = m_N} (t) = \int_{R_1} d ^3\mathbf{r}_1 \int_{R_2} d ^3\mathbf{r}_2\cdots \int_{R_N} d ^3\mathbf{r}_N \left | \Psi\left (\mathbf{r}_1 \cdots \mathbf{r}_N,m_1\cdots m_N,t \right ) \right |^2</math>