Geodesic
Local scale transformation method for the ground state of many-particle systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 55 (1983) no. 3, pp. 407-418 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A variational method is constructed that reduces the many-particle problem for the ground state of a quantum-mechanical system to the solution of one equation for the function of a local scale transformation. A theorem is proved that provides a rigorous basis of the widely used density functional method. For a fairly general form of the Hamiltonian of the system, stationarity equations are obtained explicitly together with a condition under which the solution minimizes the energy of the system. The possibility of practical application of the method is discussed. 
@article{TMF_1983_55_3_a6,
     author = {I. Zh. Petkov and M. V. Stoitsov},
     title = {Local scale transformation method for the ground state of many-particle systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {407--418},
     year = {1983},
     volume = {55},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_55_3_a6/}
}
TY  - JOUR
AU  - I. Zh. Petkov
AU  - M. V. Stoitsov
TI  - Local scale transformation method for the ground state of many-particle systems
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1983
SP  - 407
EP  - 418
VL  - 55
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1983_55_3_a6/
LA  - ru
ID  - TMF_1983_55_3_a6
ER  - 
%0 Journal Article
%A I. Zh. Petkov
%A M. V. Stoitsov
%T Local scale transformation method for the ground state of many-particle systems
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1983
%P 407-418
%V 55
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1983_55_3_a6/
%G ru
%F TMF_1983_55_3_a6
I. Zh. Petkov; M. V. Stoitsov. Local scale transformation method for the ground state of many-particle systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 55 (1983) no. 3, pp. 407-418. http://geodesic.mathdoc.fr/item/TMF_1983_55_3_a6/

[1] Messia A., Kvantovaya mekhanika, t. 2, Nauka, M., 1979, 254 pp. | MR

[2] Hohenberg P., Kohn W., Phys. Rev., B136 (1964), 864 | DOI | MR

[3] Bruekner K. A. et al., Phys. Rev., 171 (1968), 1188 ; Lombard K. A., Ann. Phys., 77 (1973), 380 ; Stock H., Nucl. Phys., A237 (1975), 365 ; Holzwarth G., Eckart G., Z. Phys., A281 (1977), 385 | DOI | DOI | DOI

[4] De Witt B. S., Rev. Mod. Phys., 29 (1957), 377 ; Phys. Rev., 85 (1953), 653 ; Nakai Sh., Progr. Theor. Phys., 13 (1955), 380 | DOI | MR | DOI | DOI | MR | Zbl

[5] Bell J. S., Lecture Notes on the Many Body Problem from the First Bergen, International School of Physics, N.-Y., 1961, 214; Eger F., Gross E., Ann. Phys., 24 (1963), 63 ; Gross E. P., Mathematical Methods in Solid State and Superfluid Theory, N.-Y., 1968, 46 | DOI | MR | DOI

[6] Eger F. M., Gross E. P., Nuovo Cim., 34 (1964), 1225 ; J. Math. Phys., 6 (1965), 891 ; 7 (1966), 578 ; Gross E. P., Ann. Phys., 62 (1971), 320 ; Witriol N. M., J. Math. Phys., 11 (1970), 669 ; 12 (1971), 177 ; 2467; McMachan A. K., J. Low Temp. Phys., 8 (1972), 159 ; Trickey S. B. et al., Phys. Rev., A7 (1973), 1662 | DOI | MR | DOI | MR | DOI | MR | DOI | DOI | DOI | DOI | DOI

[7] Pontryagin L. S., Obyknovennye differentsialnye uravneniya, Nauka, M., 1970 | MR

[8] Epstein S. T., Hirschfelder J. O., Phys. Rev., 123 (1961), 1495 | DOI | Zbl

[9] Hirschfelder J. O., J. Chem. Phys., 33 (1960), 1462 | DOI | MR

[10] Petkov I. Zh., Stoitsov M. V., Preprint R4-82-385, OIYaI, Dubna, 1982

[11] Petkov I. Zh., Stoitsov M. V., Doklady BAN, 33 (1980), 1623

[12] Petkov I. Zh., Stoitsov M. V., Preprint IG/80/34, ICTP, Trieste, 1980