TY - JOUR

T1 - Stokes' phenomenon at second-order pole and reflectionless potentials

AU - Slavyanov, S.

AU - Lay, W.

PY - 1990/12/1

Y1 - 1990/12/1

N2 - Some classes of analytic potentials with second-order poles and corresponding asymptotic solutions of the Schrodinger equation are studied. The main goal of the analysis is to answer the question as to whether a Stokes phenomenon and therefore a reflection takes place for those equations. It is shown that one can notice the Stokes phenomenon not only in the leading term of an asymptotic expansion but also in higher-order ones. Therefore for only a restricted set of potentials proposed, the reflection coefficient is exactly equal to zero although it looks like that for other potentials in the first approximation. This letter gives rise to a further extension of the original approach of Berry and Howls (1990).

AB - Some classes of analytic potentials with second-order poles and corresponding asymptotic solutions of the Schrodinger equation are studied. The main goal of the analysis is to answer the question as to whether a Stokes phenomenon and therefore a reflection takes place for those equations. It is shown that one can notice the Stokes phenomenon not only in the leading term of an asymptotic expansion but also in higher-order ones. Therefore for only a restricted set of potentials proposed, the reflection coefficient is exactly equal to zero although it looks like that for other potentials in the first approximation. This letter gives rise to a further extension of the original approach of Berry and Howls (1990).

UR - http://www.scopus.com/inward/record.url?scp=36149035458&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/23/15/006

DO - 10.1088/0305-4470/23/15/006

M3 - Article

AN - SCOPUS:36149035458

VL - 23

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 15

M1 - 006

ER -