- Bethe ansatz
In
physics , the Bethe Ansatz is a method for finding the exact solutions of certain one-dimensional quantum many-body models. It was invented byHans Bethe in 1931 to find the exact eigenvalues and eigenvectors of the one-dimensional antiferromagneticHeisenberg model Hamiltonian. The exact solutions of the so-called "s-d" model (by P.B. Wiegmann [P.B. Wiegmann, "Soviet Phys. JETP Lett.", 31, 392 (1980).] in 1980 and independently by N. Andrei, [N. Andrei, "Phys. Rev. Lett.", 45, 379 (1980). [http://prola.aps.org/abstract/PRL/v45/i5/p379_1 APS] ] also in 1980) and the Anderson model (by P.B. Wiegmann [P.B. Wiegmann, "Phys. Lett." A 80, 163 (1981). [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVM-46MTXJ3-JM&_user=10&_coverDate=11%2F24%2F1980&_alid=764316663&_rdoc=1&_fmt=high&_orig=search&_cdi=5538&_sort=d&_docanchor=&view=c&_ct=1&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=4179c84450cf05d07855b0efc67c5ed9 ScienceDirect] ] in 1981, and by N. Kawakami an A. Okiji [N. Kawakami, and A. Okiji, "Phys. Lett." A 86, 483 (1981). [http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVM-46V0M51-34&_user=10&_coverDate=12%2F14%2F1981&_alid=764317058&_rdoc=1&_fmt=high&_orig=search&_cdi=5538&_sort=d&_docanchor=&view=c&_ct=1&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=deaa5d7127069d8f862d6b3445677683 ScienceDirect] ] in 1981) are also both based on the Bethe Ansatz.[Der] "
Ansatz " [The letter "s" is pronounced as "z".] (plural: "Ansätze" — in most, but not all, English texts "Ansatzs"), which means "beginnings", "base", and "statement", is a German word that is widely encountered in physics and mathematics literature. An "ansatz" may thus refer to an assumed, but meaningful, form for a mathematical function that is not based on any underlying theory or principle. In this context, "ansatz" has the same meaning as the English word "conjecture". Since "ansatz" is anoun , in German texts the initial "a" of this word is always capitalised.Notes
References
* H. Bethe, "Zur Theorie der Metalle. I. Eigenwerte und Eigenfunktionen der linearen Atomkette." (On the theory of metals. I. Eigenvalues and eigenfunctions of the linear atom chain), Zeitschrift für Physik A, Vol. 71, pp. 205-226 (1931). [http://www.springerlink.com/content/g86x6317566uh2x6/?p=117253c6cceb4697a6a1a22ad95e1ea3&pi=6 SpringerLink] .
External links
* [http://www.phys.uri.edu/~gerhard/introbethe.html Introduction to the Bethe Ansatz]
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