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In the paper, the full-core plus correlation (FCPC) and the minimizing the expectation value of the Hamiltonian method is extended to calculate the non-relativistic energies and the wave functions of 1s22s states for the lithium-like systems from Z=21 to 30. The mass-polarization and the relativistic correction included the kinetic-energy correction, the Darwin term, the electron-electron contact term, and the orbit-orbit interaction are calculated perturbatively as first-order correction. The contribution from quantum electrodynamic (QED) is also included by using the effective nuclear charge formula. The ionization potential and term energies of the ground states 1s22s are given and compared with other's theoretical calculation and experimental results. It is shown that the FCPC methods are also effective to theoretical calculation of the ionic structure for high nuclear ion of lithium-like systems.

In noncommutative space, we examine the problem of a noninteracting and harmonically trapped Bose-Einstein condensate, and derive a simple analytic expression for the effect of spatial noncommutativity on energy spectrum of the condensate. It indicates that the ground-state energy incorporating the spatial noncommutativity is reduced to a lower level, which depends upon the noncommutativity parameter θ. The gap between the noncommutative space and commutative one for the ground-state level of the condensate should be a signal of spatial noncommutativity.

The triple differential cross section for Ar（3p6） in the special geometry of coplanar large energy loss and close to minimum momentum transfer has been calculated with the modified distorted wave Born approximation （DWBA）. The polarization interaction between the electron and the target, especially in the near-target region, and the post-collision interactions are included in the calculation. The theoretical results with modified DWBA are compared with the recent experimental data, the standard DWBA and DWBA-G. It is shown that the polarization are very important in the calculation of TDCS in coplanar asymmetric （e,2e） reaction.

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