Representation of the Coulomb Matrix Elements by Means of Appell Hypergeometric Function F2

被引：3

作者：

Bentalha, Zine el Abidine ^{[1
]}

机构：

[1] Univ Tlemcen, Theoret Phys Lab, BP 230, Tilimsen 13000, Algeria

来源：

MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY | 2018年 / 21卷 / 02期

关键词：

Quantum Hall fluid; Electron gas; Hypergeometric functions; Appell functions;

D O I：

10.1007/s11040-018-9267-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Exact analytical representation for the Coulomb matrix elements by means of Appell's double series F-2 is derived. The finite sum obtained for the Appell function F-2 allows us to evaluate explicitly the matrix elements of the two-body Coulomb interaction in the lowest Landau level. An application requiring the matrix elements of Coulomb potential in quantum Hall effect regime is presented.

引用

页数：10

共 50 条

[21] A Higher Order Painleve System in Two Variables and Extensions of the Appell Hypergeometric Functions, F1, F2 and F3
Suzum, Takao
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 2018, 61 (01): : 81 - 107
[22] SOLUTIONS IN SPECIAL CASE OF PARTIAL DIFFERENTIAL EQUATIONS ASSOCIATED WITH APPELL FUNCTION F2
OLSSON, POM
ARKIV FOR FYSIK, 1964, 25 (05): : 473 - &
[23] f1:: a code to compute Appell's F1 hypergeometric function
Colavecchia, FD
Gasaneo, G
COMPUTER PHYSICS COMMUNICATIONS, 2004, 157 (01) : 32 - 38
[24] HYPERGEOMETRIC FUNCTIONS OF 2X2 MATRIX ARGUMENT ARE EXPRESSIBLE IN TERMS OF APPELL FUNCTIONS F4
KOORNWINDER, T
SPRINKHUIZENKUYPER, I
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 70 (01) : 39 - 42
[25] Exact numerical values of diagonal matrix elements ⟨rk⟩nl, as n ≤ 8 and -7 ≤ k ≤ 4, and the symmetry of Appell's function F2(1,1)
Tarasov, VF
INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2004, 18 (23-24): : 3177 - 3184
[26] On some formulas for the Appell function F2(a, b, b′; c, c′; w; z)
Brychkov, Yu A.
Saad, Nasser
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2014, 25 (02) : 111 - 123
[27] CERTAIN SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS ASSOCIATED WITH APPELLS HYPERGEOMETRIC FUNCTION F2
OLSSON, OM
ARKIV FOR FYSIK, 1965, 29 (03): : 285 - &
[28] CONNECTION FORMULAS AND IRREDUCIBILITY CONDITIONS FOR APPELL'S F2
Kato, Mitsuo
KYUSHU JOURNAL OF MATHEMATICS, 2012, 66 (02) : 325 - 363
[29] MATRIX-ELEMENTS OF COULOMB GREENS FUNCTION
SUFFCZYNSKI, M
SWIERKOWSKI, L
BULLETIN DE L ACADEMIE POLONAISE DES SCIENCES-SERIE DES SCIENCES MATHEMATIQUES ASTRONOMIQUES ET PHYSIQUES, 1975, 23 (07): : 807 - 810
[30] On the Analytic Continuation of Appell's Hypergeometric Function F2 to Some Symmetric Domains in the Space <mml:semantics><mml:msup>C2</mml:msup></mml:semantics>
Dmytryshyn, Roman
SYMMETRY-BASEL, 2024, 16 (11):

← 1 2 3 4 5 →