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 required 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.
CITATION STYLE
Deng, Q. (2022). Isogeometric Analysis of Bound States of a Quantum Three-Body Problem in 1D. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 13351 LNCS, pp. 333–346). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-08754-7_42
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