Geodesic
Estimate of the perturbation of the eigenvalues of a two-particle Schrödinger operator with a hard-core potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 6 (1971) no. 2, pp. 225-229 
A. M. Pyzh'yanov. Estimate of the perturbation of the eigenvalues of a two-particle Schrödinger operator with a hard-core potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 6 (1971) no. 2, pp. 225-229. http://geodesic.mathdoc.fr/item/TMF_1971_6_2_a7/
@article{TMF_1971_6_2_a7,
     author = {A. M. Pyzh'yanov},
     title = {Estimate of~the~perturbation of~the~eigenvalues of~a~two-particle {Schr\"odinger} operator with a~hard-core potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {225--229},
     year = {1971},
     volume = {6},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1971_6_2_a7/}
}
TY  - JOUR
AU  - A. M. Pyzh'yanov
TI  - Estimate of the perturbation of the eigenvalues of a two-particle Schrödinger operator with a hard-core potential
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1971
SP  - 225
EP  - 229
VL  - 6
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1971_6_2_a7/
LA  - ru
ID  - TMF_1971_6_2_a7
ER  - 
%0 Journal Article
%A A. M. Pyzh'yanov
%T Estimate of the perturbation of the eigenvalues of a two-particle Schrödinger operator with a hard-core potential
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1971
%P 225-229
%V 6
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1971_6_2_a7/
%G ru
%F TMF_1971_6_2_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

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|, $a>0$, $V_M(x)=\min_x\{M,V(x)\}$, and $M$ is a sufficiently large positive number.

[1] F. Riss, B. Sekefalvi-Nad, Lektsii po funktsionalnomu analizu, IL, 1954 | MR

[2] J. M. J. VanLeenwen, A. S. Reiner, Physica, 27 (1961), 99 | DOI | MR

[3] R. Laughin, B. L. Scott, Phys. Rev., 171 (1968), 1196 | DOI

[4] M. G. Fuda, Phys. Rev., 178 (1969), 1682 | DOI

[5] I. V. Amirkhanov, O. Lkhagva, Z. K. Smedarchina, Preprint R-4-4863, OIYaI, 1969

[6] L. Shiff, Kvantovaya mekhanika, IL, 1959

[7] T. Kato, Perturbation theory for linear operators, Springer-Verlag, Berlin–Heideberg, New-York, 1966 | MR

[8] A. A. Arsenev, Preprint R5-4928, OIYaI, 1970

[9] M. Kac, “On some connections between probability theory and differential and integral equations”, Proc. Soc. Berkely. Symp. Math. Stat. and Prob. Berkely, 1951, 189 ; Matematika, 1:2 (1957), 96 | MR | Zbl

[10] I. M. Gelfand, A. M. Yaglom, Usp. mat. nauk, 11 (1956), 77 | Zbl

[11] D. Ray, Trans. Amer. Math. Soc., 77 (1954), 299 | DOI | MR | Zbl