Few-body quantum method in a d-dimensional space

• Published in: Physics letters. A 2019-06, Vol.383 (17), p.2021-2027
• Main Authors: Garrido, E., Jensen, A.S., Álvarez-Rodríguez, R.
• Format: Article
• Language: English
• Subjects: Confinement of quantum systems; d-dimensional calculations
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2019.04.007

In this work we investigate the continuous confinement of quantum systems from three to two dimensions. Two different methods will be used and related. In the first one the confinement is achieved by putting the system under the effect of an external field. This method is conceptually simple, although, due to the presence of the external field, its numerical implementation can become rather cumbersome, especially when the system is highly confined. In the second method the external field is not used, and it simply considers the spatial dimension d as a parameter that changes continuously between the ordinary integer values. In this way the numerical effort is absorbed in a modified strength of the centrifugal barrier. Then the technique required to obtain the wave function of the confined system is precisely the same as needed in ordinary three dimensional calculations without any confinement potential. The case of a two-body system squeezed from three to two dimensions is considered, and used to provide a translation between all the quantities in the two methods. Finally we point out perspectives for applications on more particles, different spatial dimensions, and other confinement potentials. •We present a novel formulation of a quantum mechanical treatment of trapped systems.•The systems are described assuming they are in a non-integer dimensional space.•For the two-body case, the equivalence between systems in a d-dimensional space and confinement in a 3D-space is shown.•This allows applications entirely within the simple method but with practical translation to the ordinary method.•For s-waves the method is universal, independent of the short-distance properties of the short-range two-body interaction.