Exact Analytical Solution of the Schrödinger Equation for an N-Identical Body-Force System

Nir Barnea

Hangshadhar Rajbongshi

J. Besprosvany, M. Moshińsky

We find the solution of the Schr\"odinger equation for the case of a central square well (or barrier) plus a centrifugal tensor well potential for a system of two spin one-half particles. The wave function is derived and from it a scattering amplitude is obtained explicitly.

Moritz Brütting, Thomas Trepl, Daniel de las Heras +1 more

, 174108) to a one-dimensional Hooke's helium model atom. The physical dynamics are described on the one-body level beyond the density-based adiabatic approximation. We show that gradients of both the microscopic velocity and acceleration field are required to correctly describe the effects due to interparticle interactions. We validate the proposed analytical forms of the superadiabatic force and transport contributions by comparison to one-body data from exact numerical solution of the Schrödinger equation. Superadiabatic contributions beyond the adiabatic approximation are important in the dynamics and they include effective dissipation.

Alexander O. Gogolin, Christophe Mora, Reinhold Egger

We revisit the problem of three identical bosons in free space, which exhibits a universal hierarchy of bound states (Efimov trimers). Modeling a narrow Feshbach resonance within a two-channel description, we map the integral equation for the three-body scattering amplitude to a one-dimensional Schrödinger-type single-particle equation, where an analytical solution of exponential accuracy is obtained. We give exact results for the trimer binding energies, the three-body parameter, the threshold to the three-atom continuum, and the recombination rate.

Zhong-Qi Ma