Wigner surmise

In mathematical physics, the Wigner surmise is a statement about the probability distribution of the spaces between points in the spectra of nuclei of heavy atoms. It was proposed by Eugene Wigner in probability theory.[1] The surmise was a result of Wigner's introduction of random matrices in the field of nuclear physics. The surmise consists of two postulates:

• In a simple sequence (spin and parity are same), the probability density function for a spacing is given by,

${\displaystyle p_{w}(s)={\frac {\pi s}{2}}e^{-\pi s^{2}/4}.}$

Here, ${\displaystyle s={\frac {S}{D}}}$ where S is a particular spacing and D is the mean distance between neighboring intervals.[2]

• In a mixed sequence (spin and parity are different), the probability density function can be obtained by randomly superimposing simple sequences.