### Abstract

Original language | English |
---|---|

Pages (from-to) | 527-539 |

Number of pages | 13 |

Journal | Theoretical and Mathematical Physics |

Volume | 183 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 |

### Fingerprint

### Cite this

}

**SCHRODINGER OPERATOR WITH A SUPERPOSITION OF SHORT-RANGE AND POINT POTENTIALS.** / Gradusov, V. A.; Yakovlev, S. L.

Research output

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

JF - Theoretical and Mathematical Physics

SN - 0040-5779

IS - 1

ER -