We present a method for solving trapped few-body problems and apply it to
three equal-mass particles in a one-dimensional harmonic trap, interacting via
a contact potential. By expressing the relative Hamiltonian in Jacobi
cylindrical coordinates, i.e. the two-dimensional version of three-body
hyperspherical coordinates, we discover an underlying C6vβ symmetry.
This symmetry simplifies the calculation of energy eigenstates of the full
Hamiltonian in a truncated Hilbert space constructed from the trap Hamiltonian
eigenstates. Particle superselection rules are implemented by choosing the
relevant representations of C6vβ. We find that the one-dimensional
system shows nearly the full richness of the three-dimensional system, and can
be used to understand separability and reducibility in this system and in
standard few-body approximation techniques.Comment: 27 pages, 5 figures, 6 tables, 37 references, 4 footnotes, 1 article;
v2 has revised introduction and results sections as well as typos correcte