We study a heavy-heavy-light three-body system confined to one space dimension. Both binding energies and corresponding wave functions are obtained for (i) the zero-range, and (ii) two finiterange attractive heavy-light interaction potentials. In case of the zero-range potential, we apply the method of Skorniakov and Ter-Martirosian to explore the accuracy of the Born-Oppenheimer approach. For the finite-range potentials, we solve the Schrödinger equation numerically using a pseudospectral method. We demonstrate that when the two-body ground state energy approaches zero, the three-body bound states display a universal behavior, independent of the shape of the interaction potential.

The following errors was introduced during the production process. In section 1.3. Outline the final two sentences should be interchanged and read 'In appendix C we derive the asymptotic behavior of the maximum mean value F sG =F sG (c) for the coherent superposition of two squeezed Gaussian states. We conclude in appendix D by describing the model of the dissipation of a quantum state via interaction with a reservoir at zero temperature.' instead of 'We conclude in appendix D by describing the model of the dissipation of a quantum state via interaction with a reservoir at zero temperature. In appendix C we derive the asymptotic behavior of the maximum mean value F sG =F sG (c) for the coherent superposition of two squeezed Gaussian states.' Also, reference [14] has an error in the year of publication. It should read 'Straka I, Lachman L, Hloušek J, Miková M, Mičuda M, Ježek M and Filip R 2018 npj Quantum Inf. 4 4' not 'Straka I, Lachman L, Hloušek J, Miková M, Mičuda M, Ježek M and Filip R 2016 npj Quantum Inf. 4 4'.

Sufficient condition for a quantum state to be genuinely quantum non-Gaussian L Happ, M A Efremov, H Nha et al. -Geometry of the Quantum States of Light in a Mach-Zehnder Interferometer