Simon problems

In mathematics, the Simon problems (or Simon's problems) are a series of fifteen questions posed in the year 2000 by <a href="/facts/Barry_Simon/BImmcE2I">Barry Simon</a>, an American mathematical physicist. Inspired by other collections of mathematical problems and open conjectures, such as the <a href="/facts/Hilbert_problems/HaQWIxvV">famous list</a> by <a href="/facts/David_Hilbert/1vhlHn4b">David Hilbert</a>, the Simon problems concern <a href="/facts/Operator_(physics)/rCJw8UFz">quantum operators</a>. Eight of the problems pertain to anomalous <a href="/facts/Spectrum_(functional_analysis)/cA1evTo6">spectral</a> behavior of Schrödinger operators, and five concern operators that incorporate the <a href="/facts/Coulomb_potential/Nmqm6hm5">Coulomb potential</a>. 
In 2014, <a href="/facts/Artur_Avila/QMeAHXcQ">Artur Avila</a> won a <a href="/facts/Fields_Medal/khFmkEnm">Fields Medal</a> for work including the solution of three Simon problems. Among these was the problem of proving that the set of energy levels of one particular abstract quantum system was, in fact, the <a href="/facts/Cantor_set/6NUcMJvN">Cantor set</a>, a challenge known as the "Ten Martini Problem" after the reward that <a href="/facts/Mark_Kac/AcByIKRc">Mark Kac</a> offered for solving it. 
The 2000 list was a refinement of a similar set of problems that Simon had posed in 1984.

Simon problems open-in-new

Simon problems