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Approximate but reliable solutions of a quantum system with $N$ identicalparticles can be easily computed with the envelope theory, also known as theauxiliary field method. This technique has been developed for Hamiltonians witharbitrary kinematics and one- or two-body potentials. It is adapted here forcyclic systems with $N$ identical particles, that is to say systems in which aparticle $i$ has only an interaction with particles $i-1$ and $i+1$ (with$N+1\equiv 1$).

Bound cyclic systems with the envelope theory