Geodesic
Quantum hydrodynamics of particle systems with Coulomb interaction and quantum Bohm potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 2, pp. 287-304 
L. S. Kuz'menkov; S. G. Maksimov. Quantum hydrodynamics of particle systems with Coulomb interaction and quantum Bohm potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 2, pp. 287-304. http://geodesic.mathdoc.fr/item/TMF_1999_118_2_a8/
@article{TMF_1999_118_2_a8,
     author = {L. S. Kuz'menkov and S. G. Maksimov},
     title = {Quantum hydrodynamics of particle systems with {Coulomb} interaction and quantum {Bohm} potential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {287--304},
     year = {1999},
     volume = {118},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_118_2_a8/}
}
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The quantum hydrodynamics of $N$ interacting particles with Coulomb interaction in an external electromagnetic field can be described by the field equations for the microscopic dynamics in the physical space. Macroscopic hydrodynamic equations are obtained by local averaging. Quantum corrections to the hydrodynamic equations are due to the multiparticle quantum Bohm potential. Specific properties of Fermi- and Bose-system hydrodynamics are investigated. The Cauchy-type integral for the quantum system and the corresponding one-particle Schrцdinger equation are found under the standard classical hydrodynamic assumptions.

[1] L. S. Kuzmenkov, TMF, 86:2 (1991), 231 | MR

[2] M. A. Drofa, L. S. Kuzmenkov, TMF, 108:1 (1996), 3 | DOI | Zbl

[3] L. S. Kuzmenkov, “Makroskopicheskaya struktura elektromagnitnogo polya v zadachakh elektrodinamiki i fizicheskoi kinetiki”, Plenarnyi doklad na konferentsii “Problemy fundamentalnoi fiziki” (7–12 oktyabrya 1996 g., Saratov), 1996

[4] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979, S. 32 | MR

[5] I. E. Tamm, Osnovy teorii elektrichestva, Nauka, M., 1989, S. 93–96

[6] S. Goldstein, Phys. Today, 51:3 (1998), 42 ; 4, 38 | DOI

[7] D. Bohm, Phys. Rev., 85 (1952), 166 | DOI | MR | Zbl

[8] D. Bohm, Phys. Rev., 85 (1952), 180 | DOI | MR | Zbl

[9] D. Bohm, J. P. Vigier, Phys. Rev., 96 (1954), 208 | DOI | MR | Zbl

[10] G. García de Polavieja, Phys. Lett. A, 220 (1996), 303 | DOI | MR | Zbl

[11] G. García de Polavieja, Phys. Rev. E, 55 (1997), 1451 | DOI

[12] E. Madelung, Z. Phys., 40 (1926), 332

[13] N. N. Bogolyubov, N. N. Bogolyubov (ml.), Vvedenie v kvantovuyu statisticheskuyu mekhaniku, Nauka, M., 1984 | MR

[14] S. Shveber, Vvedenie v relyativistskuyu kvantovuyu teoriyu polya, Izd-vo inostr. lit., M., 1963

[15] E. M. Lifshits, L. P. Pitaevskii, Elektrodinamika sploshnykh sred, Nauka, M., 1992

[16] S. Olaria, I. Porescu, Rev. Mod. Phys., 57:1 (1985), 339 | DOI

[17] N. N. Bogolyubov, Izbrannye trudy v trekh tomakh, Tom tretii, Naukova dumka, Kiev, 1971 | MR

[18] A. I. Akhiezer, S. V. Peletminskii, Metody statisticheskoi fiziki, Nauka, M., 1977 | MR