1 .. - // . - 1995. - T. 95(4). - C.104-112.
2 Chin C., Grimm R., Julienne P., and Tiesinga E.. Fesh bach resonances in ultracold gase // Review of Modern Physics 82. - 2010. - P.1225-1286.
3 Kohler T., Goral K., and Julienne P.S. Production of cold molecules via magnetically tunable Fesh bach resonance // Review of Modern Physics 78. - 2006. - P.1311-1361.
4 Bloch, Dalibard J., and Zwerger W. Many-body physics with ultracold gase // Review of Modern Physics 80. - 2008. - P. 885-964.
5 Yurovsky V.A., Olshanii M., and Weiss D.S. Collisions, correlations, and intagrability in atom wave guide // Advances in Atomic, Molecular, and Optical Physics 55. - 2008. P. 61-138.
6 Martiyanov K., Makhalov V., and Turlapov A. Observation of a two-dimensional Fermi gas of atom // Physical Review Letters 105. - 2010. - P.030404.
7 Zurn G., Serwane F., Lompe T., Wenz A.N., Ries M.G. Fermionization of two distinguishable fermions // Physical Review Letters 108. - 2012. -P. 075303.
8 Busch T., Englert B.-G., Rzazewski K., and Wilkens M. Two Cold Atoms in a Harmonic Trap // Found. Phys. -1998. - P. 549.
9 Olshanii M. Atomic scattering in the presence of an external confinement and a gass of impenetrable bosons // Physical Review Letters 81. - 2010. - P. 938 - 941.
10 Ni K.K., Ospelkaus S., Wang D., Quemener G., Neyenhuis B., M. H. G. de Miranda, Bohn L. Dipolar Collisions of Polar Molecules in the Quantum Regime // Nature. - 2010. P. 1324-1328.
11 .. - // - - . -2012.
12 Hu C.Y.,Melezhik V. // Phys.Rev.Lett. 90. - 2003. - P. 083202.
13 Melezhik V. S. A computational method for quantum dynamics of a three- dimensional atom in strong fields // toms and molecules in strong external fields - Eds.: P. Schmelcher and W. Schweizer- Plenum Press - New-York. -1998. P. 89-94.
14 Melezhik V. S. Polarization of harmonics generation from a hydrogen atom in a strong laser field // Phys. Lett. - A230.-1997. - P. 203208.
15 Melezhik V. S. Mathematical modeling and computational science // Lecture Notes in ComputerScience - Volume 7125 - Springer-Verlag - Berlin Heidelberg. - 2012. - P. 94107.
16 Dineykhan M., Efimov G.V., Ganbold G., Nedelko S.N. Oscillator Representation in Quantum Physics // Lecture Notes in Physics. Berlin - Springer-Verlag - 1995. - V. 26.
17 Dineykhan M., Zhaugasheva S.A., Bekbaev A. K. Determination of the energy spectrum of a three-body Coulomb system with relativistic corrections // PHYSICAL REVIEW A Volume 87, 052506, p. 1-12, 2013.
18 Ishmukhamedov I. S., Valiolda D. S., and Zhaugasheva S. A. Description of ultracold atoms in a one-dimensional geometry of a harmonic trap with a
realistic interaction // Physics of Particles and Nuclei Letters, Volume
11, Issue 3, p. 238-244 (2014).
|
|
19 .., .., .., ., қ ә қ ұқң ө // , , 2015., 3, 301 (2015), 120 125.
20 .. - // . 2006. - . 176. -C. 345-364.
21 Chin, Grimm R., Julienne P.S. and Tiesinga F.,Feshbach E. Resonances in Ultracold Gases // Rev. Mod. Phys. - 2010. - P. 82 1225.
22 Haller E., Mark M. J., Hart R., Danzl J. G., Reichsollner L., Melezhik V., Schmelcher P. and Nagerl H.C. Confinement-Induced Resonances in Low-Dimensional Quantum Systems // Phys. Rev. Lett. - 2010. - P. 153203.
23 Peng S.-G., Hu H., Liu X.-J. and Drummond P.D. Confinement-Induced Resonances in Anharmonic Waveguides // Phys. Rev A 84.-2011. - P. 043619.
24 Bergeman T., Moore M.G., Olshanii M. Atom-Atom Scattering in the Presence of a Cylindrical Harmonic Potential: Numerical Results and an Extended Analytic Theory // Phys. Rev. Lett. 2003. - P. 163201.
25 Dineykhan M., Zhaugasheva S.A., Toinbaeva N.Sh. // Jour.Phys.B: At. Mol. Opt. Phys. - 2010. Vol.43. - P.015003.
26 Saeidian S., Melezhik V.S., Schmelcher Mutlichannel P. Atomic Scattering and Confinement-Induced Resonances in Waveguides // Phys. Rev.- A 77.-2008. -P. 042721.
27 Busch T., Englert R.G., Rzazewski K. and Wilkens M. Two cold atoms in a harmonic traps // Foundations of physics 28(4). -2010. - P. 549-559.
28 Hermann M. R. and Fleck J. A. // Jr. Phys. Rev - A38.-1988.
29 Peng S.-G., Hu H., Liu X.-J. and Drummond P. Confinement-induced resonances in anharmonic waveguides // Physical Review A84.-2011. - P. 043619.
30 Shi-Guo Peng, Hui Hu, Xia-Ji Liu, Peter D. Drummond // Phys. Rev. - A 84.-2011. P. 043619.
31 .C., .., .., // , 2014 ., 11, 3 (187), . 390-400.
Қ 1
ө ә. ү ң қ
қ ә қ ң ә , қ . ұ ң , қ , . ү - қ қ ұғ қ ү . қ қ ә қ. ә , қ ң қ ққ. ү ң:
(1)
. (2.51) ң қ ң қ ә қ ү:
(2)
қ. ұғ − қ :
. (3)
ққ ұ қ ә ұқ ө ұ:
|
|
. (4)
қ ұқ ә қ ө ә ұ қ ң
. (5)
:
(6)
. ә (2.52), (2.55) , қ қ (2.51) ө ң:
(7)
ү . ққ () , , ү .
ң ң ө (Ө) ә қ қ ө, ү ү . ә :
(8)
ү қ. (2.57) ң ң (2.58) қ, қ ү, :
(9)
. ң ө ә ққ :
(10)
ү. ү ү қ. ү ә :
; (11)
қ. (2.60) ү (2.59) қ, қ қ , қ ү :
(12)
ұғ . (2.60) үң ә (2.59) ң − ө ғ қ. қ ү. Ө ә − ө ң ө ү. ң қ () .
. (13)
(2.63) ө қ ң қғ. ң ғқ ң қ қ. (2.63) ң Ө ә қ ққ:
. (14)
ңң . , - . ұ ә ө ә . ұ ә қ ө ң ә қ қ. ү :
(15)
ү . ұғ - ң . ұ ә қ ү қ , ә , - ә ө. ү қғ :
1) қғ ү ғ, ң ғ ;
2) Қғ ү ә қ ң қ ү ң ө ң . ұ Ө әң .
ғ ә қ ә қ ө:
(16)
(2.64) ң ғ (2.66) қ, қ ү . ә қ қ ө, қ, :
(17)
қ қ ү қ. қ :
(18)
(19)
ү . ұғ − ң
|
|
, (20)
, − ө ң, ө қ :
. (21)
- ә ү ө ң. ә қ ү қғ ү - ө , - ң қ,
. (22)
ң
. (23)
ғқ ң қ :
. (24)
ұ ә ң қ . қ ү ү ә ң қ ө.
[1] ң -ұ үң ғ