| 词条 | Simon problems |
| 释义 |
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.[1][2] Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators.[3] In 2014, Artur Avila won a Fields Medal for work including the solution of three Simon problems.[4][5] 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.[5][6] Eight of the problems pertain to anomalous spectral behavior of Schrödinger 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.[7][8] See also
External links
References1. ^{{cite book|last=Simon |first=Barry |chapter=Schrödinger Operators in the Twenty-First Century | title=Mathematical Physics 2000 |publisher=Imperial College London |isbn=978-1-86094-230-3 |doi=10.1142/9781848160224_0014 |year=2000}} {{math-stub}}2. ^{{cite journal|title=Dynamics and Spectral Theory of Quasi-Periodic Schrödinger-type Operators |first1=C. A. |last1=Marx |first2=S. |last2=Jitomirskaya |journal=Ergodic Theory and Dynamical Systems |volume=37 |pages=2353—2393 |year=2017 |arxiv=1503.05740 |doi=10.1017/etds.2016.16}} 3. ^{{cite web|url=http://www.math.pku.edu.cn/teachers/gansb/conference09/Damanik-Minicourse-2009-08-09.pdf |title=Dynamics of SL(2,R)-Cocycles and Applications to Spectral Theory; Lecture 1: Barry Simon’s 21st Century Problems |first=David |last=Damanik |access-date=2018-07-07 |website=Beijing International Center for Mathematical Research, Peking University}} 4. ^{{cite web|url=http://www2.cnrs.fr/en/2435.htm?debut=8&theme1=12 |title=Fields Medal awarded to Artur Avila |website=Centre national de la recherche scientifique |date=2014-08-13 |access-date=2018-07-07}} 5. ^1 {{cite web|url=https://www.theguardian.com/science/alexs-adventures-in-numberland/2014/aug/13/fields-medals-2014-maths-avila-bhargava-hairer-mirzakhani |title=Fields Medals 2014: the maths of Avila, Bhargava, Hairer and Mirzakhani explained |website=The Guardian |last=Bellos |first=Alex |date=2014-08-13 |access-date=2018-07-07}} 6. ^{{cite web|last=Tao |first=Terry |title=Avila, Bhargava, Hairer, Mirzakhani |url=https://terrytao.wordpress.com/2014/08/12/avila-bhargava-hairer-mirzakhani/ |website=What's New |date=2014-08-12 |access-date=2018-07-07 |author-link=Terence Tao}} 7. ^{{cite book|last=Simon |first=Barry |chapter=Fifteen problems in mathematical physics |title=Perspectives in Mathematics: Anniversary of Oberwolfach 1984 |year=1984 |publisher=Birkhäuser |pages=423–454}} 8. ^{{cite arxiv|last=Coley |first=Alan A. |title=Open problems in mathematical physics |eprint=1710.02105 }} 3 : unsolved problems in mathematics|Unsolved problems in physics|Mathematical physics |
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