Geodesic
Regularization of the equations of the quantum theory for a~scalar neutral field with selfinteraction in the case of two spatial degrees of freedom
Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 3, pp. 355-364

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

The method developed earlier [1] is applied to the more complicated case of two spatial coordinates. The equations for the ground and excited states are of the same form as in the one-dimensional case, but the integrations are substituted by double ones. The divergencies more complicated than those in the one-dimensional case arise. However they can be avoided by means of extracting a certain special factor from the eigen-functional $\Omega$ of the energy operator $H$. 
@article{TMF_1971_9_3_a5,
     author = {L. G. Zastavenko},
     title = {Regularization of the equations of the quantum theory for a~scalar neutral field with selfinteraction in the case of two spatial degrees of freedom},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {355--364},
     publisher = {mathdoc},
     volume = {9},
     number = {3},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a5/}
}
TY  - JOUR
AU  - L. G. Zastavenko
TI  - Regularization of the equations of the quantum theory for a~scalar neutral field with selfinteraction in the case of two spatial degrees of freedom
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1971
SP  - 355
EP  - 364
VL  - 9
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a5/
LA  - ru
ID  - TMF_1971_9_3_a5
ER  - 
%0 Journal Article
%A L. G. Zastavenko
%T Regularization of the equations of the quantum theory for a~scalar neutral field with selfinteraction in the case of two spatial degrees of freedom
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1971
%P 355-364
%V 9
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a5/
%G ru
%F TMF_1971_9_3_a5
L. G. Zastavenko. Regularization of the equations of the quantum theory for a~scalar neutral field with selfinteraction in the case of two spatial degrees of freedom. Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 3, pp. 355-364. http://geodesic.mathdoc.fr/item/TMF_1971_9_3_a5/