Symmetries in the many-body problems, a method to find its analytical solution, and Helium atom spectrum
In this work it is shown that there are symmetries beyond the Euclidean group $E\left(3\right)$ in 3-body problem, and by extension in many-body problem, with inverse squared distance inter particle force. The symmetries in 3-body problem form a group: $SO\left(4\times3,2\times3\right)/\left(C\left(...
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
26.01.2024
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| Subjects | |
| Online Access | Get full text |
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| Summary: | In this work it is shown that there are symmetries beyond the Euclidean group
$E\left(3\right)$ in 3-body problem, and by extension in many-body problem,
with inverse squared distance inter particle force. The symmetries in 3-body
problem form a group:
$SO\left(4\times3,2\times3\right)/\left(C\left(3\times2\right)\right)$, where
$C\left(n\right)$ is the planar translation group in n dimensions, which forms
its Spectrum-Generating group. Some of these quantities commute with the
Hamiltonian. The existence of these conserved quantities was verified by
calculating energy spectrum of the Helium atom. This method can also be used to
find symmetries in many-body problem, and to calculate energy levels, and
wave-functions of more complicated systems, which include every possible atomic
and molecular systems in chemistry. |
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| DOI: | 10.48550/arxiv.2401.15019 |