Abstract
A modification of the Rayleigh—Ritz variational principle is described which makes possible a calculation of the energy, wave function, and pair distribution function
f
12
≡
f
(
x
1
,
x
2
)
of a Bose fluid, such as liquid
4
He, at absolute zero. The assumptions made are: (i) two-body interactions with potential U
ij
, (ii) trial wave functions of the form
f
12
≡
f
(
x
1
,
x
2
)
and (iii) the Kirkwood ‘superposition' approximation. Under these approximations, the expectation energy is
E
=
1
2
n
2
∫
∫
d
3
X
1
d
3
X
2
f
12
U
12
−
h
2
m
−
1
(
∇
1
8
ϕ
12
)
+
(
∇
1
ϕ
12
)
2
+
n
∫
d
3
X
2
f
13
f
23
ϕ
12
⋅
∇
1
ϕ
13
,
where
n
≡
N/V
. It is shown here that making
E
stationary with respect to
independent
variations in
f
and
ɸ
corresponds to simultaneously applying the ordinary Rayleigh-Ritz principle and solving the Born-Green-Yvon integral equation for
f
. The method is illustrated by reproducing Bogolyubov’s results for the case where
U
is small. The case where
U
is large must be dealt with numerically, but transformations for simplifying the computations are given here.
Cited by
6 articles.
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