Estimate of the perturbation of the eigenvalues of a two-particle Schrödinger operator with a hard-core potential

A. M. Pyzh'yanov


Abstract: An estimate is obtained for $|\lambda_i-\lambda_i^M|$, where $\lambda_i$ and $\lambda_i^M$ are, respectively, the eigenvalues of the operators $H=-\Delta+V(x)$ and $H_M=-\Delta+V_M(x)$, $x=(x_1,x_2,x_3)$, the function $V(x)$ is singular for $|x|<a$, $a>0$, $V_M(x)=\min_x\{M,V(x)\}$, and $M$ is a sufficiently large positive number.

Received: 13.05.1970

 English version: Theoretical and Mathematical Physics, 1971, 6:2, 165–168

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