Isogeometric Analysis of Bound States of a Quantum Three-Body Problem in 1D

• URL: http://arxiv.org/abs/2202.09986v2
• Date: Thu, 31 Mar 2022 00:50:39 GMT
• Title: Isogeometric Analysis of Bound States of a Quantum Three-Body Problem in 1D
• Authors: Quanling Deng
• Abstract summary: We represent the wavefunctions by linear combinations of B-spline basis functions and solve the problem as a matrix eigenvalue problem. The eigenvalue gives the eigenstate energy while the eigenvector gives the coefficients of the B-splines that lead to the eigenstate. We demonstrate through various numerical experiments that IGA provides a promising technique to solve the three-body problem.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we initiate the study of isogeometric analysis (IGA) of a quantum three-body problem that has been well-known to be difficult to solve. In the IGA setting, we represent the wavefunctions by linear combinations of B-spline basis functions and solve the problem as a matrix eigenvalue problem. The eigenvalue gives the eigenstate energy while the eigenvector gives the coefficients of the B-splines that lead to the eigenstate. The major difficulty of isogeometric or other finite-element-method-based analyses lies in the lack of boundary conditions and a large number of degrees of freedom for accuracy. For a typical many-body problem with attractive interaction, there are bound and scattering states where bound states have negative eigenvalues. We focus on bound states and start with the analysis for a two-body problem. We demonstrate through various numerical experiments that IGA provides a promising technique to solve the three-body problem.

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