The problem of normal transmission of quasiparticles through the interface of two continuous media, one of which is a quantum fluid, is solved. The quantum fluid is described as a continuous medium with correlations. Within the framework of this approach the dispersion relation of the quantum fluid Ω(k) can be arbitrary. The integral equation describing it in a half-space is solved by the Wiener–Hopf method, and its general solution is obtained. This approach is applied to the dispersion relation of the Bose–Einstein condensate. It is shown that the solutions of equations of quantum fluid in a half-space are traveling waves deformed near the border by specific surface standing waves. By means of boundary conditions the general solution in the whole space is obtained. Expressions for transmission and reflection factors of waves in both directions are derived, depending on their frequency. The results are important for describing the creation of helium II phonons on the boundary with a solid, and are of interest for classical acoustics.

1.
A. F. G.
Wyatt
,
N. A.
Lockberie
, and
R. A.
Sherlock
,
Phys. Rev. Lett.
33
,
1425
(
1974
).
2.
M. A. H.
Tucker
and
A. F. G.
Wyatt
,
Science
283
,
1150
(
1999
).
3.
I. M.
Khalatnikov
,
An Introduction to the Theory of Superfluidity
,
Addison-Wesley
, New York (
1998
).
4.
N. N.
Bogoliubov
,
J. Phys. (USSR)
11
,
23
(
1947
);
reprinted in
D.
Pines
,
The Many Body Problem
,
Benjamin
, New York (
1961
).
5.
C. J.
Pethick
and
H.
Smith
,
Bose-Einstein Condensation in Dilute Gases
,
Cambridge University Press
, Cambridge (
2002
).
6.
L.
Pitaevskii
and
S.
Stringari
,
Bose-Einstein Condensation
,
Clarendon Press
, Oxford (
2003
).
7.
R. V.
Vovk
,
C. D. H.
Williams
, and
A. F. G.
Wyatt
,
Phys. Rev. B
68
,
134508
(
2003
).
8.
R. V.
Vovk
,
C. D. H.
Williams
, and
A. F. G.
Wyatt
,
Phys. Rev. Lett.
91
,
235302
(
2003
).
9.
I. N.
Adamenko
,
K. E.
Nemchenko
,
V. A.
Slipko
, and
A. F. G.
Wyatt
,
Fiz. Nizk. Temp.
30
,
579
(
2004
).
I. N.
Adamenko
,
K. E.
Nemchenko
,
V. A.
Slipko
, and
A. F. G.
Wyatt
, [
Low Temp. Phys.
30
,
432
(
2004
)].
10.
I. N.
Adamenko
,
K. E.
Nemchenko
,
V. A.
Slipko
, and
A. F. G.
Wyatt
,
J. Phys.: Condens. Matter
17
,
2859
(
2005
).
11.
L. M.
Brekhovskikh
,
Waves in Layered Media
,
Academic Press
, New York (
1960
), USSR Academy of Sciences Press, Moscow (1957), Nauka, Moscow (1973).
12.
L. I.
Mandelshtamm
,
Lectures in Optics, Relativity, and Quantum Mechanics
[in Russian],
Nauka
, Moscow (
1972
).
13.
P. K.
Schelling
,
S. R.
Phillpot
, and
P.
Keblinski
,
Appl. Phys. Lett.
80
,
2484
(
2002
).
14.
P. K.
Schelling
and
S. R.
Phillpot
,
J. Appl. Phys.
93
,
5377
(
2003
).
15.
I. N.
Adamenko
,
K. E.
Nemchenko
, and
I. V.
Tanatarov
,
Phys. Rev. B
67
,
104513
(
2003
).
16.
L.
Pitaevskii
and
S.
Stringari
,
Phys. Rev. B
45
,
13133
(
1992
).
17.
I. N.
Adamenko
,
K. E.
Nemchenko
, and
I. V.
Tanatarov
,
J. Low Temp. Phys.
138
,
10909
005
1584
9
(
2005
).
18.
F. D.
Gakhov
,
Boundary Value Problems
,
Addison-Wesley
, Reading, Mass. (1966), Gos. Izdat. Fiz-Mat. Lit., Moscow (1958).
19.
R.
Mittra
and
S. W.
Lee
,
Analytical Techniques in the Theory of Guided Waves
,
MacMillan
, New York (
1971
).
20.
I. N.
Adamenko
,
K. E.
Nemchenko
, and
I. V.
Tanatarov
,
J. Mol. Liq.
120
(
1–3
),
167
(
2005
).
21.
S. M.
Rytov
,
Zh. Éksp. Teor. Fiz.
17
,
930
(
1947
).
22.
Ya. L.
Alpert
,
Izv. Akad. Nauk SSSR, Ser. Fiz.
12
,
241
(
1948
).
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