Geodesic
Elastic scattering and the~path integral
Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 3, pp. 367-386

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From the stationary Schrödinger equation in the framework of nonrelativistic quantum mechanics, we derive a representation of the elastic scattering amplitude in the form of a path integral. For evaluating the path integrals, we propose a method called unitary approximation. We obtain the scattering lengths and cross sections for a rectangular potential, a singular repulsive potential, and the Yukawa potential and compare with the exact results.
Keywords: quantum mechanics, elastic scattering, path integral. 
@article{TMF_2014_179_3_a5,
     author = {G. V. Efimov},
     title = {Elastic scattering and the~path integral},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {367--386},
     publisher = {mathdoc},
     volume = {179},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_179_3_a5/}
}
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G. V. Efimov. Elastic scattering and the~path integral. Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 3, pp. 367-386. http://geodesic.mathdoc.fr/item/TMF_2014_179_3_a5/