Energy Spectrum of Two-Particle Cruciform Quantum Wires

We analyze the energy spectrum of a heterostructure with two particles separated in two crossed wires with parabolic confinement along their axes. We show that the energy spectrum in the limit of extremely strong confinement does not depend on the type of the interaction, and it is similar to the spectrum of a harmonic oscillator. On the contrary, when the confinement is very weak, the two-particle energy spectra for the cases of attraction and repulsion are very different. We present curves for the dependence of the energy levels on the lengths of the wires.