Based on the theory of point transformations, a possible exact relationship between the atomic electron densities in momentum and position spaces is studied through the inverse mapping from the electron density to the N‐electron wave function with an appropriate generator or reference N‐electron wave function. The results are used to construct the ground‐state energy density functional of atoms in momentum space.

1.
R. Benesch and V. H. Smith, Jr., in Wave Mechanics—The First Fifty Years, edited by W. C. Price, S. S. Chissick, and T. Ravensdale (Butterworths, London, 1973), pp. 357–377.
2.
P. Kaijser and V. H. Smith, Jr., in Quantum Science. Methods and Structure, edited by J.‐L. Calais, O. Goscinski, J. Linderberg, and Y. Öhrn (Plenum, New York, 1976), pp. 417–425.
3.
V. H. Smith, Jr., in Electron and Magnetization Densities in Molecules and Crystals, edited by P. Becker (Plenum, New York, 1980), pp. 3–25.
4.
B. G. Williams, Compton Scattering: The Investigation of Electron Momentum Distributions (McGraw‐Hill, New York, 1977).
5.
E. S.
Kryachko
and
T.
Koga
,
Adv. Quantum Chem.
17
,
97
(
1985
).
6.
J.
Oddershede
and
J. R.
Sabin
,
Chem. Phys.
71
,
161
(
1982
);
T.
Koga
and
M.
Morita
,
Theor. Chim. Acta
61
,
73
(
1982
);
A.
Harmalker
,
A. M.
Simas
,
V. H.
Smith
,Jr.
, and
W. M.
Westgate
,
Int. J. Quantum Chem.
23
,
811
(
1983
);
A. M.
Simas
,
V. H.
Smith
,Jr.
, and
A. J.
Thakkar
,
Int. J. Quantum Chem. Symp.
18
,
385
(
1984
);
A. J.
Thakkar
,
J. Chem. Phys.
81
,
1943
(
1984
);
A. J.
Thakkar
,
A. N.
Tripathi
, and
V. H.
Smith
, Jr.
,
Phys. Rev. A
29
,
1108
(
1984
).
7.
M.
Cooper
,
Adv. Phys.
20
,
453
(
1971
);
N. L.
Allan
and
N. H.
March
,
Int. J. Quantum Chem. Symp.
17
,
227
(
1983
);
F. M.
Mueller
,
Phys. Rev. B
15
,
3039
(
1977
);
R.
Benesch
,
J. Phys. B
9
,
2587
(
1976
);
I. R.
Epstein
,
Phys. Rev. A
8
,
160
(
1973
).
8.
P. A. M. Dirac, The Principle of Quantum Mechanics (Oxford University, London, 1958).
9.
C. A.
Coulson
,
Mol. Phys.
26
,
507
(
1973
);
I. R.
Epstein
,
Phys. Rev. A
8
,
160
(
1973
).
10.
C. T.
Corcoran
and
P. W.
Langhoff
,
J. Math. Phys.
18
,
651
(
1977
);
E. S.
Kryachko
and
T.
Koga
,
J. Math. Phys.
28
,
8
(
1987
).
11.
I. R.
Epstein
and
W. L.
Lipscomb
,
J. Chem. Phys.
53
,
4418
(
1970
).
12.
D. C.
Rawlings
and
E. R.
Davidson
,
J. Phys. Chem.
89
,
969
(
1985
).
13.
G.
Burkhardt
,
Ann. Phys. (Leipzig)
,
26
,
567
(
1936
).
14.
A.
Konya
,
Acta Phys. Hung.
1
,
12
(
1949
).
15.
C. A.
Coulson
and
N. H.
March
,
Proc. Phys. Soc. London Ser. A
63
,
367
(
1950
).
16.
S. R.
Gadre
and
R. K.
Pathak
,
Phys. Rev. A
24
,
2906
(
1981
);
R. K.
Pathak
and
S. R.
Gadre
,
J. Chem. Phys.
74
,
5925
(
1981
);
S. R.
Gadre
and
R. K.
Pathak
,
J. Chem. Phys.
77
,
1073
(
1982
).,
J. Chem. Phys.
17.
S. R.
Gadre
,
S. P.
Gejji
, and
R. K.
Pathak
,
Phys. Rev. A
27
,
3328
(
1983
);
S. R.
Gadre
,
S.
Chakravorty
, and
R. K.
Pathak
,
J. Chem. Phys.
78
,
4581
(
1983
).
18.
R. K.
Pathak
,
S. P.
Gejji
, and
S. R.
Gadre
,
Phys. Rev. A
29
,
3402
(
1984
);
S. R.
Gadre
and
S. P.
Gejji
,
J. Chem. Phys.
80
,
1175
(
1984
).
19.
S. R.
Gadre
and
S. P.
Gejji
,
Chem. Phys. Lett.
109
,
584
(
1984
);
S. R.
Gadre
and
S. P.
Gejji
,
112
,
45
(
1984
); ,
Chem. Phys. Lett.
S. R.
Gadre
,
R. D.
Bendale
, and
S. P.
Gejji
,
Chem. Phys. Lett.
117
,
138
(
1985
).
20.
A. J.
Thakkar
,
J. Chem. Phys.
76
,
748
(
1982
);
W. M.
Westgate
,
A. M.
Simas
, and
V. H.
Smith
, Jr.
,
J. Chem. Phys.
83
,
4054
(
1985
).
21.
L.
Lam
and
P. M.
Platzman
,
Phys. Rev. B
9
,
5128
(
1974
);
J.
Callaway
and
N. H.
March
,
Solid State Phys.
38
,
135
(
1984
);
V. H. Smith, Jr., in Local Density Approximations in Quantum Chemistry and Solid State Physics, edited by J. P. Dahl and J. Avery (Plenum, New York, 1984), pp. 1–19.
22.
I. Z.
Petkov
,
M. V.
Stoitsov
, and
E. S.
Kryachko
,
Int. J. Quantum Chem.
29
,
149
(
1986
);
E. S.
Kryachko
and
E. V.
Ludeña
,
Phys. Rev. A
35
,
957
(
1987
);
E. S. Kryachko and E. V. Ludeña, The Energy Density Functional Theory of Many‐Electron Systems (Reidel‐Kluwer, Dordrecht, 1988).
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