Geodesic
Uniform asymptotic solution in the~form of an~Airy function for semiclassical bound states in one-dimensional and radially symmetric problems
Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 3, pp. 382-414

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider stationary scalar and vector problems for differential and pseudodifferential operators leading to the appearance of asymptotic solutions of one-dimensional problems localized in a neighborhood of intervals (“bound states”). Based on the semiclassical approximation and the Maslov canonical operator, we develop a constructive algorithm that allows writing an asymptotic solution globally under certain conditions using an Airy function of complex argument.
Keywords: semiclassical asymptotic solution, bound state, closed trajectory, WKB approximation, canonical operator, Airy function. 
@article{TMF_2019_201_3_a6,
     author = {A. Yu. Anikin and S. Yu. Dobrokhotov and V. E. Nazaikinskii and A. V. Tsvetkova},
     title = {Uniform asymptotic solution in the~form of {an~Airy} function for semiclassical bound states in one-dimensional and radially symmetric problems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {382--414},
     publisher = {mathdoc},
     volume = {201},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_201_3_a6/}
}
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A. Yu. Anikin; S. Yu. Dobrokhotov; V. E. Nazaikinskii; A. V. Tsvetkova. Uniform asymptotic solution in the~form of an~Airy function for semiclassical bound states in one-dimensional and radially symmetric problems. Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 3, pp. 382-414. http://geodesic.mathdoc.fr/item/TMF_2019_201_3_a6/