Nondirect product discrete variable representation in multidimensional quantum problems

Abstract

We have developed a method for treating different quantum few-body dynamics without traditional partial-wave analysis. The key element of the method is a nondirect product discrete variable representation (npDVR) we have suggested and developed in application to the time-dependent mutidimensional Schrödinger equations. It happened that this approach was very efficient in quantitative analysis of low-dimensional ultracold few-body systems arising in confined geometry of atomic traps. As an example, we consider the numerical analysis of the four-dimensional Schrödinger equation describing the resonant molecule formation in confined two-component atomic mixture with transferring the energy release to the center-ofmass excitation of forming molecules.