Analytical results for the Morse potential in s-wave ultracold scattering: three dimensional vs. one dimensional problem

Details Analytical results for the Morse potential in s-wave ultracold scattering: three dimensional vs. one dimensional problem Analytical results for the Morse potential in s-wave ultracold scattering: three dimensional vs. one dimensional problem

2012-03-06

arxiv.org/abs/1203.1285v1

Physics

Quantum Physics

5 pages, 3 figures

Scientific paper

Taking advantage of the known analytic expression of the eigenfunctions and eigenenergies of the Morse Hamiltonian, explicit expressions are found for the scattering length $a$ and the effective range $r_e$ which determine the s-wave scattering of ultracold atoms. The effects on $a$ and $r_e$ of considering the radial coordinate in the interval $[0,\infty)$ or in the extended region $(-\infty, \infty)$ are studied in detail.

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