Uniform Asymptotic Solutions of a System of two Schrödinger Equations with Potential-Curve-Crossing Point

Irina Jakushina

doi:10.1088/0305-4470/28/6/024

paper

Uniform Asymptotic Solutions of a System of two Schrödinger Equations with Potential-Curve-Crossing Point

arXiv:hep-th/9404161 · doi:10.1088/0305-4470/28/6/024

Abstract

A formal uniform asymptotic solution of the system of differential equations $h^{2} \frac{d ^{2} U _{1}}{d z ^{2}} + Φ_{1} U_{1} = α U_{2}$ , $h^{2} \frac{d ^{2} U _{2}}{d z ^{2}} + Φ_{2} U_{2} = α U_{1}$ , for $z \in D$ and for h real, large is obtained, when D contains curve-crossing point. Asymptotic approximations for the solutions are constructed in terms of parabolic cylinder functions. Analytical properties of the expansion's coefficients are investigated.The case of potantial barier is also considered.

arXiv comment16 pages, LaTex, UUITP 9/94