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SCHRODINGER OPERATOR WITH A SUPERPOSITION OF SHORT-RANGE AND POINT POTENTIALS. / Gradusov, V. A.; Yakovlev, S. L.
в: Theoretical and Mathematical Physics, Том 183, № 1, 2015, стр. 527-539.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - SCHRODINGER OPERATOR WITH A SUPERPOSITION OF SHORT-RANGE AND POINT POTENTIALS
AU - Gradusov, V. A.
AU - Yakovlev, S. L.
PY - 2015
Y1 - 2015
N2 - We study the class of Schrodinger operators whose potential terms are sums of the short-range V (r) and point potentials. We consider the case where the short-range potential has a singularity on the support r = 0 of the point interaction. The point interaction is constructed using the asymptotic form of the Green's function of the Schrodinger operator -Delta+V (r) with a short-range potential V as r -> 0. We consider potentials with a singularity of the form r(-rho), rho > 0, at the origin. We use the Lippmann-Schwinger integral equation in our study. We show that if the singularity of the potential is weaker than the Coulomb singularity, then the asymptotic behavior of the Green's function has a standard singularity. If the singularity of the potential has the form r(-rho), 1
AB - We study the class of Schrodinger operators whose potential terms are sums of the short-range V (r) and point potentials. We consider the case where the short-range potential has a singularity on the support r = 0 of the point interaction. The point interaction is constructed using the asymptotic form of the Green's function of the Schrodinger operator -Delta+V (r) with a short-range potential V as r -> 0. We consider potentials with a singularity of the form r(-rho), rho > 0, at the origin. We use the Lippmann-Schwinger integral equation in our study. We show that if the singularity of the potential is weaker than the Coulomb singularity, then the asymptotic behavior of the Green's function has a standard singularity. If the singularity of the potential has the form r(-rho), 1
UR - https://link.springer.com/article/10.1007%2Fs11232-015-0279-x
U2 - 10.1007/s11232-015-0279-x
DO - 10.1007/s11232-015-0279-x
M3 - Article
VL - 183
SP - 527
EP - 539
JO - Theoretical and Mathematical Physics (Russian Federation)
JF - Theoretical and Mathematical Physics (Russian Federation)
SN - 0040-5779
IS - 1
ER -
ID: 4034295