Analytic solutions of topologically disjoint systems

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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 delta-function 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.
Translated title of the contributionAnalytic solutions of topologically disjoint systems
Original languageEnglish
Article number085301
JournalJournal of Physics A: Mathematical and Theoretical
Issue number8
Publication statusPublished - 28 Jan 2015

    Research areas

  • quant-ph

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