Analytical Structure Matching and Very Precise Approach to the Coulombic Quantum Three—Body Problem

A powerful approach to solve the Coulombic quantium three-body problem is proposed.The approach is expeonentially convergent and more efficient than the hyperspherical coordinate method and the correlaion-function hyperspherical harmonic method.This approach is numerically competitive with the variational methods.Such as that using the Hylleraas-type basis functions,Numerical comparisons are made to demonstrate the efficiency of this approach,by calculating the nonrelativistic and infinite-nuclear-mass limit of the ground state energy of the helium atom.The exponential convergency of this approach is due to the full matching between the analytical structure of the basis functions that are used in thuis paper and the true wavefunction.This full matching was not reached by most other methods.For example,the variational method using the Hylleraas-type basis does not reflects the logarithmic singularity of the true wavefunction at the origin as predicted by Bartlett and Fock.Two important approaches are proposed in this work to reach this full matching:the coordinate transfomation method and the asymptotic series method.Besides these,this work makes use of the least square method to substitute complicated numerical integrations in solving the Schroedinger equation without much loss of accuracy,which is routinely used by people to fit a theoretical curve with discrete experimental data,but here is used to simplify the computation.     

BCS Ground State and XXZ Antiferromagnetic Model as SU（2）,SU（1,1） Coherent States：AN Algebraic Diagonalization Method

An algebraic diagonalization method is proposed.As two examples,the Hamiltonians of BCS ground state under mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized by using SU(2),SU(1,1) Lie algebraic method,respectively.Meanwhile,the eignenstates of the above two models are revealed to be SU(2),SU(1,1) coherent states,respectively,The relation between the usual Bogoliubov-Valatin transformation and the algebraic method in a special case is also discussed.     

多体关联Green函数动力学Ⅱ.等时极限

对多体关联Green函数的基本动力学方程组作等时极限,得到了密度矩阵形式的多体关联动力学方程组,并证明了各种不同时序的等时极限间的等价性.