*Huang and Klein, op. cit. in Java

Print qr barcode in Java *Huang and Klein, op. cit.
*Huang and Klein, op. cit.
Encode qrcode for java
using java toembed quick response code for asp.net web,windows application
Barcode encoder with java
using java toassign bar code on asp.net web,windows application
Fig. 13.10 Experimental liquid structure fac-
scanning barcode in java
Using Barcode decoder for Java Control to read, scan read, scan image in Java applications.
tor (Fourier transform of pair correlation function) of liquid He 4 .
Control qr bidimensional barcode image on .net c#
generate, create qr code none with c# projects
Control qr code 2d barcode size with .net
to generate qr code jis x 0510 and qrcode data, size, image with .net barcode sdk
13.11 Comparison between the calculated excitation spectrum (solid curve) and measurements (dashed curve).
Qr-codes barcode library in .net
using visual studio .net crystal todraw qr code 2d barcode for asp.net web,windows application
gives an excitation energy as function of k shown in Fig. 13.11, which reproduces the roton part of the spectrum qualitatively. *
Access bar code with java
generate, create bar code none with java projects
Dilute Bose gases have become accessible to experiments, furnishing us with simpler examples of superfluids. Among these are spin-aligned atomic hydrogen gas,t and liquid He 4 adsorbed in porous Vycor glass.:j: At sufficiently low temperatures, the interparticle potential may be summarized by only one parameter, the scattering length, which is a kind of effective hard-sphere diameter. The low-lying energy levels of a dilute Bose gas then correspond to those of a hard-sphere gas, which can be treated through the methods of pseudopotentials introduced in Section 10.5.
Control ansi/aim code 39 data on java
to connect 3 of 9 and uss code 39 data, size, image with java barcode sdk
*An improved wave function that fits the data better is given by R. P. Feynman and M. Cohen, Phys. Rev. 102,1189 (1956). iT. J. Greytak and D. Kleppner, in New Trends in Atomic Physics, Vol. II (Les Houches 38) G. Greyberg and R. Stora, eds. (North-Holland, Amsterdam, 1984). tB. C. Crooker, B. Hebral, E. N. Smith, and J. D. Reppy, Phys. Rev. Lett. 51, 666 (1983). T. D. Lee, K. Huang, and C. N. Yang, Phys. Rev. 106,1135 (1957); see also K. Huang, op. cit.
Control barcode standards 128 size for java
to create code 128a and code128 data, size, image with java barcode sdk
QR Code 2d Barcode drawer in java
using barcode generation for java control to generate, create quick response code image in java applications.
Effective Hamiltonian
Barcode maker in java
using java tocreate bar code on asp.net web,windows application
The Hamiltonian is
Receive isbn for java
using barcode printing for java control to generate, create bookland ean image in java applications.
.Yt'= - 2m
Barcode Data Matrix implement for .net
using barcode integration for sql reporting service control to generate, create data matrix barcodes image in sql reporting service applications.
L 'il/ + j=l
.net Winforms bar code integrating for .net
use .net for windows forms bar code development todisplay barcode with .net
Generate gs1 128 on .net
generate, create uss-128 none in .net projects
Gs1 Datamatrix Barcode generating with .net
use rdlc data matrix barcodes creator toattach gs1 datamatrix barcode with .net
where a is the hard-sphere diameter. We can re-express it in the quantized field representation as
.net Vs 2010 ean-13 supplement 5 integration for .net
using barcode printer for .net framework control to generate, create ean13+2 image in .net framework applications.
(13.871 where
Control code-128 data with .net
code128b data in .net
l/J(r) =
!TT '
(13.88 1
and we have imposed periodic boundary conditions:
when n is a vector whose components are independently 0, 1, 2, .... The appearance of the operator (ajar)r seems to complicate things, but actually the effect is quite simple. The operator has the property that
a; [rj(r)] r-O = j(O)
ar [rj(r)] r=O = 0
(if j is regular at r ( if j----+ r-->or
The operator (ajar)r weeds out, so to speak, any singularity of the Ijr type in the function to which it is applied. * We treat the interaction as a perturbation on the ideal gas. The validity of the Hamiltonian is restricted by the conditions
ajv 1/ 3 1,
ha 1
where v is the specific volume, and k is any wave number of an excited particle in the unperturbed state. For low-lying excited states, we assume (13.92 )
"cf. Problem 10.7.
First we decompose the interaction into a part that has only diagonal matrix elements with respect to the unperturbed free-particle states and a part that has only off-diagonal elements. The part with diagonal matrix elements has been worked out and given in (A.36) of the Appendix, and discussed in Section 10.5. For the off-diagonal elements, we isolate a part that contains terms proportional to aoao or aiab. What is left contains terms both proportional to and independent of a o or ai. The matrix elements of the first part are of order N larger than those of the remaining part, which will be neglected. Thus we have
2m.Yt' = L>2a!a
+ 87TaN
(1 - ~ ~:n~) 2N
L' (atataoa o + akakabai) k
Now we replace both aoao and abai by N, and obtain an effective Hamiltonian:
2m~ff =
The sum
47TaN +
I' [(k
+ 87Ta) ata k + 47Ta (ata~k + aka- k )] (13.94)
in (13.93) and (13.94) is defined by
I' fk ==
!...-(r I Jr
In practice, this operation affects only the ground state energy, and has the effect of subtracting out the term proportional to a 2 .
Energy Levels
To diagonalize (13.94) we introduce a linear transformation first used by Bogolubov* : 1 a k = ~ (b k - akb~k) 1 - a~ (13.96) 1 at = ~ (bt - akb_ k ) 1 - a~ or
bk =
~ (a k + aka~k)
1 - a~ 1 1 - a~
~ (at + aka_ k )
where a is assumed to be a real number than one. It is clear that b k and bt
*N. N. Bogolubov. J. Phys. USSR 11,23 (1947).
satisfy the same commutation rules as
[b k , b k ,] =
at, namely
(13.98 I
[bt, bt,] =
[b k , btl
Therefore b k and bt can be interpreted, respectively, as annihilation and creatior. If we substitute (13.96) into the effective Hamilto operators, just as k and nian (13.94), we find that ~ff is diagonalized by choosing