### Abstract

We describe a procedure to solve an up to 2N problem where the particles are separated topologically in N groups with at most two particles in each. Arbitrary interactions are allowed between the (two) particles within one group. All other interactions are approximated by harmonic oscillator potentials. The problem is first reduced to an analytically solvable N-body problem and N independent two-body problems. We calculate analytically spectra, wave functions, and normal modes for both the inverse square and deltafunction two-body interactions. In particular, we calculate separation energies between two strings of particles. We find that the string separation energy increases with N and interaction strength.

Original language | English (US) |
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Article number | 085301 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 48 |

Issue number | 8 |

DOIs | |

State | Published - Feb 27 2015 |

### Keywords

- exactly solvable models
- few-body systems
- harmonic expansion

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*48*(8), [085301]. https://doi.org/10.1088/1751-8113/48/8/085301