U - U _ w(p) J J V in Java

Integrated qr codes in Java U - U _ w(p) J J V
U - U _ w(p) J J V
Qr Barcode barcode library on java
using barcode drawer for java control to generate, create qr code iso/iec18004 image in java applications.
(5.3.61a)
Bar Code generation with java
using java toinclude bar code on asp.net web,windows application
be the coherent Green's operator and let
Bar Code barcode library with java
Using Barcode decoder for Java Control to read, scan read, scan image in Java applications.
(5.3.61b)
Control denso qr bar code data in .net c#
qr code iso/iec18004 data with .net c#
be the modified potential operator for each scatterer. Then (5.3.60) becomes
Qrcode barcode library on .net
using web form touse qr barcode on asp.net web,windows application
(5.3.62)
QR Code 2d Barcode barcode library in .net
using visual .net crystal toconnect qr-codes with asp.net web,windows application
G = Gc + Gc
Control qr code data with vb.net
to insert qr barcode and qr codes data, size, image with visual basic.net barcode sdk
"' U G
Use barcode for java
generate, create bar code none on java projects
(5.3.63)
Java pdf417 integration in java
use java barcode pdf417 writer toincoporate pdf417 for java
is the N-particle scattering equation. Equation (5.3.63) is analogous to the -original N-particle scattering equation, with Go replaced by G c and U j replaced by U j' The new transition operator is
Control code128 size on java
code 128 size on java
(5.3.64)
Control ean / ucc - 14 image on java
use java ean 128 generating toinsert gs1-128 on java
The process of taking configurational averages and truncating the hierarchy of equations can be repeated, giving new dispersion relations. However, theHe new dispersion relations depend on the choice of the coherent potential operator w(p), which has not yet been determined. The consistent choice for w(P) or the coherent potential choice is choosing w(p) such that
Data Matrix 2d Barcode encoding with java
using java torender ecc200 for asp.net web,windows application
(5.3.65)
Java isbn - 13 generating in java
use java isbn - 13 creator todisplay bookland ean on java
Hence, the final result of the averaged Green'H operator is equal to the original coherent Green's operator. The coherent potential shall be introduced into the effective field approximation and the quasi-crystalline approximation.
Asp.net Aspx Crystal qr code implementation with vb.net
generate, create qr-codes none with vb.net projects
3.4 Coherent Potential (CP)
Bar Code barcode library on .net
generate, create bar code none on .net projects
Effective Field Approximation with Coherent Potential (EFA-CP)
Control pdf417 2d barcode image for visual basic
use visual .net pdf417 writer topaint pdf417 on vb.net
When the effective field approximation is applied to the N-particle scattering equation (5.3.63) in a manner completely analogous to Section 3.2, with Ge playing the role of Go and fJ playing the role of U, the result for the averaged Green's operator in momentum representation is
Control code 39 full ascii size on visual basic.net
to produce 3 of 9 and barcode code39 data, size, image with vb barcode sdk
G{p)
Control pdf 417 image in office excel
using barcode development for excel control to generate, create pdf417 image in excel applications.
[G~1 (p) _ no1'p{p,P)] -1
.net Winforms pdf 417 integrated in .net
using winforms todeploy barcode pdf417 with asp.net web,windows application
(5.3.66)
Code-128c barcode library with c#.net
using barcode maker for visual .net control to generate, create barcode code 128 image in visual .net applications.
The coherent potential choice of w{p) is such that (5.3.65) is satisfied, which, in view of (5.3.66), imposes the condition (5.3.67) That is, the momentum representation of T with both arguments equal to p is zero. By using (5.3.61b) and l' = fJ + l' G e fJ it follows that l' = 'fij(P) +
l' G e (U - 'fij;))
so that
~ = ~ -1 w p TGeG +v =
where
(=I+TGe) = : -= U
(5.3.68)
c = (G~1 + ~ )
Define
(5.3.69)
t that satisfies the Lippmann-Schwinger equation
i=u+uci
(1' GeC -1
Simplifying we get
(5.3.70)
Eliminating U from (5.3.68) and (5.3.70) and using (5.3.69), we have
+ ~)
(1 + c i)
i + l' GJ
and then
(1 - wp{p)G\i c Ge V e w PC GV 'LX)
-1 _
(5.3.71a)
5 MULTIPLE SCATTERING THEORY FOR DISCRETE SCATTERERS
We take in momentum representation and define (pIC elp1) -
= Ce(P)(plp1)
and (pIGlp1) = G(P)(plp1)' To normalize the resulting equation, we multiply by (l/V) e-i(P-Pl) rj and integrate over Mj, noting that J Mj(l/V) e-i(P-Pl) rJ = (P!P1)/V and J Mj = V. Thus
Tp(p,p) =
[G~1 (p) G(p) lp(p,p) - W(p)]
G(p) G~1 (p)
(5.3.71b)
Hence, the coherent potential condition of Tp(p, p) = 0 implies that w(P) =
Ge (p)G(p)tp(p,p). Furthermore, by taking V ---t 00 in (5.3.69), and noting that wpCe(p) remains finite, we have G(p) ---t Ce(p). Thus the choice of
coherent potential is
W(p) = tp(p,p)
(5.3.72)
Hence, the final results for the averaged Green's operator are (5.3.61a) with
w(p) given by (5.3.72). The quantity t satisfies (5.3.70), the momentum representation of which becomes (on letting V ---t (0) lp(P1,P2) = Up(P1,P2) +
J(~):3
Up(PllP3) Ge(P3)lp(P3,P2)
(5.3.73)
The dispersion relation for EFA-CP is det Since G e depends on (5.3.73) is nonlinear.
[G~l (p) -
nJp(p,p)] = 0
(5.3.74)
via (5.3.61a) and (5.3.72), the integral equation
3.5 Quasi-crystalline Approximation with Coherent Potential (QCA-CP) The quasi-crystalline approximation can be applied to the N-particle scattering equation (5.3.63). Manipulations are performed as in Section 3.3 with
Ge playing the role of Go and
averaged Green's operator is
playing the role of U. The result for the
G(P) =
where
[G~1 (p) _ nocp(p,P)] -1
(5.3.75)
(5.3.76)
3.5 QCA-CP
Putting
in terms of U j , we have
(5; =
Ce if
j.7i'j
Uj -
df/q(r/-rj)Uj Gi5/-
df/q(r/-rj) ~Gi5/
(5.3.77)
e-i'j).'i'j
Taking (5.3.77) in momentum representation and noting that gives
C p(pI,p2) = UP(pI' 152) +
where
J(~)3
UP(pI' p3)Gc(p3)qp(p3 - p2)Cp (p3, 152)
(5.3.78)
~ P, PI Cp(- -) =
[=1 + 'Wp(p) Gc (-) qp (- - PI . C-p(- -) + 'Wp(p) (-1-) (5 .. 79) 3 P P -)] P, PI P PI
---v-
---v-
Next, use (5.3.79) to express C p in terms of Cpo We obtain
Cp(p, PI) =
[I + 'W~p) Gc(p)qp(p - PI)] Cp(p, pd _[I + 'W~p) Gc(p)qp(O)] 'W~p) (15 I PI)
(5.3.80)
Putting (5.3.80) in (5.3.78), we then have
Cp(pI' 152) = U P(pI ,p2)G c(p2)
J(~)3
[I + Wp~2) Gc(p2)qp(0)
r G~\p2)
U P(pI' p3)Gc(p3)qp(p3 - 152)
. [1 +
= 'WP(p3)=
Gc(p3)qp(p3 - 152)
=-1 _
] -1::::Cp(p3,p2)
(5.3.81)
The QCA approximation gives (5.3.82) G (15) = G c (15) - noCp(p,p) For coherent potential condition to apply, we choose 'W p such that
Cp(p,P) = 0
(5.3.83)
which we will impose on (5.3.79). To normalize properly (5.3.79), we use the technique as in EFA-CP by multiplying both sides of the equation with (ljV)e- i (p-p\).r j and integrating over dfj . Hence, (5.3.79) becomes
Cp(p, 15) =
[I + 'W~p)
Gc(P) qp(O)] Cp(p, 15) + 'Wp(p)
(5.3.84)