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Update to v0.2

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Added: Discussion of uniqueness of the solution of the Simple Equation

  Added: Exercise: prove \psi_0>=0 using |\psi_0|

  Added: Links in bibliography

  Removed: Commented blocks

  Fixed: Formatting
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Ian Jauslin
2023-07-26 15:57:58 -05:00
parent e76604e394
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3 changed files with 92 additions and 60 deletions
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@ -29,7 +29,8 @@ doi:{\tt\color{blue}\href{http://dx.doi.org/10.4007/annals.2020.192.3.5}{10.4007
\bibitem[FS23]{FS23}S. Fournais, J.P. Solovej - {\it The energy of dilute Bose gases II: the general case}, Inventiones mathematicae, volume\-~232, issue\-~2, pages\-~863-994, 2023,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/s00222-022-01175-0}{10.1007/s00222-022-01175-0}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2108.12022}{2108.12022}}.\par\medskip
\bibitem[Ga99]{Ga99}G. Gallavotti - {\it Statistical mechanics, a short treatise}, Springer, 1999.\par\medskip
\bibitem[Ga99]{Ga99}G. Gallavotti - {\it Statistical mechanics, a short treatise}, Springer, 1999,\par\penalty10000
{\tt\color{blue}\href{https://141.108.10.74/pagine/deposito/1998/libro.pdf}{https://141.108.10.74/pagine/deposito/1998/libro.pdf}}.\par\medskip
\bibitem[Ja22]{Ja22}I. Jauslin - {\it Review of a Simplified Approach to study the Bose gas at all densities}, The Physics and Mathematics of Elliott Lieb, The\-~90th Anniversary Volume I, chapter\-~25, pages\-~609-635, ed. Rupert L. Frank, Ari Laptev, Mathieu Lewin, Robert Seiringer, EMS Press, 2022,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.4171/90-1/25}{10.4171/90-1/25}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/2202.07637}{2202.07637}}.\par\medskip
@ -68,7 +69,8 @@ doi:{\tt\color{blue}\href{http://dx.doi.org/10.4171/90-2/40}{10.4171/90-2/40}},
\bibitem[Se11]{Se11}R. Seiringer - {\it The Excitation Spectrum for Weakly Interacting Bosons}, Communications in Mathematical Physics, volume\-~306, issue\-~2, pages\-~565-578, 2011,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/s00220-011-1261-6}{10.1007/s00220-011-1261-6}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/1008.5349}{1008.5349}}.\par\medskip
\bibitem[Te14]{Te14}G. Teschl - {\it Mathematical Methods in Quantum Mechanics With Applications to Schr\"odinger Operators}, Second Edition, Graduate Studies in Mathematics, volume\-~157, AMS, 2014.\par\medskip
\bibitem[Te14]{Te14}G. Teschl - {\it Mathematical Methods in Quantum Mechanics With Applications to Schr\"odinger Operators}, Second Edition, Graduate Studies in Mathematics, volume\-~157, AMS, 2014,\par\penalty10000
{\tt\color{blue}\href{https://www.mat.univie.ac.at/~gerald/ftp/book-schroe/schroe2.pdf}{https://www.mat.univie.ac.at/$\sim$gerald/ftp/book-schroe/schroe2.pdf}}.\par\medskip
\bibitem[YY09]{YY09}H. Yau, J. Yin - {\it The Second Order Upper Bound for the Ground Energy of a Bose Gas}, Journal of Statistical Physics, volume\-~136, issue\-~3, pages\-~453-503, 2009,\par\penalty10000
doi:{\tt\color{blue}\href{http://dx.doi.org/10.1007/s10955-009-9792-3}{10.1007/s10955-009-9792-3}}, arxiv:{\tt\color{blue}\href{http://arxiv.org/abs/0903.5347}{0903.5347}}.\par\medskip