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Correlation in Momentum Space of Tonks-Girardeau Gas

We investigate the correlation properties of the ground state of Tonks-Gigrardeal gases in the momentum space. With Bose-Fermi mapping method the exact ground state wavefunction in coordinate space can be obtained basing on the wavefunction of spin-polarized Fermions. By Fourier transformation we obtain the ground state wavefunction in momentum space, and therefore the momentum distribution, pair correlation and the reduced one-body density matrix (ROBDM) in momentum space. The ROBDM in momentum space is the Fourier transformation of the ROBDM in coordinate space and the pair correlation in momentun space is the Fourier transformation of the reduced two-body density matrix in coordinate space. The correlations in momentum space display larger values only in small momentum region and vanish in most other regions. The lowest natural orbital and occupation distribution are also obtained.