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Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators. Eight of the problems pertain to anomalous spectral behavior of Schr枚dinger operators, and five concern operators that incorporate the Coulomb potential. The 2000 list was a refinement of a similar set of problems that Simon had posed in 1984." /> <meta property="og:site_name" content="DBpedia" />  </head> <body about="http://dbpedia.org/resource/Simon_problems">  <nav class="navbar navbar-expand-md navbar-light bg-light fixed-top align-items-center"> <div class="container-xl"> <a class="navbar-brand" href="http://wiki.dbpedia.org/about" title="About DBpedia" style="color: #2c5078"> <img class="img-fluid" src="/statics/images/dbpedia_logo_land_120.png" alt="About DBpedia" /> </a> <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#dbp-navbar" aria-controls="dbp-navbar" aria-expanded="false" aria-label="Toggle navigation"> </button> <div class="collapse navbar-collapse" id="dbp-navbar"> <ul class="navbar-nav me-auto mb-2 mb-lg-0"> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownBrowse" role="button" data-bs-toggle="dropdown" aria-expanded="false"> Browse 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class="col"> <div class="text-muted"> An Entity of Type: <a href="http://www.w3.org/2002/07/owl#Thing">Thing</a>, from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, within Data Space: <a href="http://dbpedia.org">dbpedia.org</a> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> In mathematics, the Simon problems (or Simon's problems) are a series of fifteen questions posed in the year 2000 by Barry Simon, an American mathematical physicist. Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators. Eight of the problems pertain to anomalous spectral behavior of Schr枚dinger operators, and five concern operators that incorporate the Coulomb potential. The 2000 list was a refinement of a similar set of problems that Simon had posed in 1984. </div> </div> </div> </section>   <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract">dbo:abstract</a> </td><td class="col-10 text-break"><ul> <li style="display:none;">Die Simon-Probleme sind eine Liste von f眉nfzehn Problemen aus der mathematischen Physik, die Barry Simon 1984 zusammenstellte und 2000 aktualisierte. Simon z盲hlte 1984 f眉nfzehn Probleme auf, die meist jeweils mehrere Teilprobleme hatten, so dass man je nach Z盲hlung auch auf 35 kommt. Einige der Probleme sind au脽erordentlich schwierige Grundlagenprobleme und einige von Simon bewusst (nach dem Vorbild einiger der Hilbertschen Probleme) sehr vage formuliert und umrei脽en eher Forschungsfelder. (de)</li> <li>In mathematics, the Simon problems (or Simon's problems) are a series of fifteen questions posed in the year 2000 by Barry Simon, an American mathematical physicist. Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators. Eight of the problems pertain to anomalous spectral behavior of Schr枚dinger operators, and five concern operators that incorporate the Coulomb potential. In 2014, Artur Avila won a Fields Medal 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 Cantor set, a challenge known as the "Ten Martini Problem" after the reward that Mark Kac offered for solving it. The 2000 list was a refinement of a similar set of problems that Simon had posed in 1984. (en)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageExternalLink">dbo:wikiPageExternalLink</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="http://mathworld.wolfram.com/SimonsProblems.html" href="http://mathworld.wolfram.com/SimonsProblems.html">http://mathworld.wolfram.com/SimonsProblems.html</a></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageID">dbo:wikiPageID</a> </td><td class="col-10 text-break"><ul> <li>57577573 (xsd:integer)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageLength">dbo:wikiPageLength</a> </td><td class="col-10 text-break"><ul> <li>23662 (xsd:nonNegativeInteger)</li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageRevisionID">dbo:wikiPageRevisionID</a> 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Simon z盲hlte 1984 f眉nfzehn Probleme auf, die meist jeweils mehrere Teilprobleme hatten, so dass man je nach Z盲hlung auch auf 35 kommt. Einige der Probleme sind au脽erordentlich schwierige Grundlagenprobleme und einige von Simon bewusst (nach dem Vorbild einiger der Hilbertschen Probleme) sehr vage formuliert und umrei脽en eher Forschungsfelder. (de)</li> <li>In mathematics, the Simon problems (or Simon's problems) are a series of fifteen questions posed in the year 2000 by Barry Simon, an American mathematical physicist. Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators. Eight of the problems pertain to anomalous spectral behavior of Schr枚dinger operators, and five concern operators that incorporate the Coulomb potential. The 2000 list was a refinement of a similar set of problems that Simon had posed in 1984. 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