Three identical bosons: Properties in noninteger dimensions and in external fields

Abstract

Three-body systems that are continuously squeezed from a three-dimensional space into a two-dimensional space are investigated. Such squeezing can be obtained by means of an external confining potential acting along a single axis. However, this procedure can be numerically demanding, or even undoable, especially for large squeezed scenarios. An alternative is provided by use of the dimension d as a parameter that changes continuously within the range 2≤d≤3. The simplicity of the d calculations is exploited to investigate the evolution of three-body states after progressive confinement. The case of three identical spinless bosons with relative s waves in three dimensions and a harmonic oscillator squeezing potential is considered. We compare results from the two methods and provide a translation between them, relating dimension, squeezing length, and wave functions from both methods. All calculations are then possible entirely within the simpler d method, but simultaneously providing the equivalent geometry with the external potential.