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2012년 11월 2일 (금) 03:05 판
introduction
- N bosons interacting on a line of length L via the delta function potential
- one-dimensional Bose gas
- 1963 Lieb and Liniger solved by Bethe ansatz
Hamiltonian
- quantum mechanical Hamiltonian
\(H=-\sum_{j=1}^{N}\frac{\partial^2}{\partial x_j^2}+2c\sum_{1\leq i<j\leq N}^{N}\delta(x_i-x_j)\)
two-body scattering term
- \(s_{ab}=k_a-k_b+ic\)
Bethe-ansatz equation
\(\exp(ik_jL)=\prod_{l=1}^{N}\frac{k_j-k_l+ic}{k_j-k_l-ic}\)
energy spectrum
\(E=\sum_{j=1}^{N}k_j^2\)
history
encyclopedia
books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
articles
- Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction
- C. N. Yang and C. P. Yang, J. Math. Phys. 10, 1115 (1969)
- Some exact results for the many-body problem in one dimension with repulsive delta-function interaction
- C.N. Yang, Phys. Rev. Lett. 19 (1967), 1312-1315
- Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
- Elliott H. Lieb and Werner Liniger, 1963
- http://www.ams.org/mathscinet
- [1]http://www.zentralblatt-math.org/zmath/en/
- [2]http://arxiv.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
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