Confinement effects on an ultra-cold matter wave-packet by a square well impurity near the de-localization threshold: analytic solutions, scaling, and width propertiesRicardo Méndez-Fragoso and Remigio Cabrera-TrujilloEur. Phys. J. D, 69 5 (2015) 139DOI: https://doi.org/10.1140/epjd/e2015-50736-1