The Legendre Collocation Spectral Method for the Ground State Solutions of the Bose-Einstein Condensates

LIU Wenjie; WANG Hanquan

doi:10.21656/1000-0887.430257

Volume 44 Issue 6

Jun. 2023

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LIU Wenjie, WANG Hanquan. The Legendre Collocation Spectral Method for the Ground State Solutions of the Bose-Einstein Condensates[J]. Applied Mathematics and Mechanics, 2023, 44(6): 719-730. doi: 10.21656/1000-0887.430257

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The Legendre Collocation Spectral Method for the Ground State Solutions of the Bose-Einstein Condensates

doi: 10.21656/1000-0887.430257

LIU Wenjie^1
,,
WANG Hanquan^{1, 2
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1.
School of Mathematics and Statistics, Yunnan University of Finance and Economics, Kunming 650221, P.R.China
2.
School of Mathematics, Yunnan Normal University, Kunming 650504, P.R.China

Received Date: 2022-08-10
Rev Recd Date: 2023-05-18
Publish Date: 2023-06-01

Abstract

Abstract

In recent years, a series of important achievements have been made in the experimental study of the ground state solutions of the Bose Einstein condensates. First, the ground state solution problem of the Bose Einstein condensate was converted into the extreme value problem of energy functional with the dimensionless method. In the discretization of the energy functional, the Legendre collocation spectral method was used in the 1D and 2D cases. Second, the energy functional minimum problem was numerically simulated. The analyses of the experimental data and graphs show that, the Legendre collocation spectral method is applicable to the ground state solution of the non-rotating Bose Einstein condensate, and the errors of the numerical results are very small.
- Bose-Einstein condensate,
- Legendre collocation spectral method,
- numerical calculation

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References(31)

References

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