SCHRODINGER OPERATOR WITH A SUPERPOSITION OF SHORT-RANGE AND POINT POTENTIALS

Research output

Abstract

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
Original languageEnglish
Pages (from-to)527-539
Number of pages13
JournalTheoretical and Mathematical Physics
Volume183
Issue number1
DOIs
Publication statusPublished - 2015

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Superposition
Singularity
operators
Operator
Range of data
Point Interactions
Green's function
Green's functions
Potential Operators
Integral Equations
Asymptotic Behavior
integral equations
interactions
Term
Form

Cite this

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title = "SCHRODINGER OPERATOR WITH A SUPERPOSITION OF SHORT-RANGE AND POINT POTENTIALS",
abstract = "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",
author = "Gradusov, {V. A.} and Yakovlev, {S. L.}",
year = "2015",
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pages = "527--539",
journal = "Theoretical and Mathematical Physics",
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T1 - SCHRODINGER OPERATOR WITH A SUPERPOSITION OF SHORT-RANGE AND POINT POTENTIALS

AU - Gradusov, V. A.

AU - Yakovlev, S. L.

PY - 2015

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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

JF - Theoretical and Mathematical Physics

SN - 0040-5779

IS - 1

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