SCIENTIFIC ABSTRACT V.A. CHALDYSHEV - A.A. CHALIKOV

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R000308120003-4
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: December 30, 2016
• Document Release Date: June 19, 2000
• Sequence Number: 3
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

88048
S/JL39/60/000/006/0.13/032
~EOWE414
Synmietry Properties~of theiSchr6ding4r-Pauli Equation for an
Electron in a Crystal
where is*the two-component-wave functiont
.0 , are the Pauli matrices, cItVa is the Levi-Civita density:
and -' V(r) is a function which is invariant with respect. to all,
the operations of the space group K. It is shown that the
time reversal operator for this equation does not' In- general
commute with Its symmetry operators., A generalization of the
Wigner theorem (Ref.3) -is.obtained",which.can be used as a-
criteriop for the existence of an additioAal degeneracy
assoclated with the isotropy of time. The connection between.' Z10
this criterion and the criterion obtained by Herring (Ref.4)
is established. The paper. Is entirely mathematical.
There are 5 non-Soviet references,
ASSOCIATION: Sibirskiy fiziko-tekhnicheakiy institut
pri Tomskom gosuniversitete-imeni V.V.Kuyby3heva
(Siberian PhysicotechnIcal Institute at
Tomsk State University imeni V.V.Kuybyahev)
SUBMITTED: October 9, 1959
_Card 2/2

341E9
S/139/62/uoo/oo6/007/023
?1d 0 (11r-3, J E039/E320
AUTHM Chaldy!"j"-V--A-
TITLE. On the question of investigating the energy spectrum
of electrons in crystals. I.
PERIODICALS- Izvestiya vysshikh uchebnykh zavedeniy, Fizika,
no. 6, ig6i, 48 - 51
TEXT: It is well known that it is possible to determine the
nature of the dependence of the electron energy from the wave
vector K with the aid of the perturbation theory. In this
work is proposed a method of determining the energy spectrum for
electrons in crystals from the wave vector without using the
perturbation theory. This means that an approximate formula for
the function E(K) is obtained for all the Brillouinzones.
The energy as a function of the wave vector K can be obtained
from a solution of the equations for the periodic part of the
wave function:
Hku = 4-)u, (10
Card 1/4

On the question of ....
3418!~
S/139/6i/ooo/o6/007/023
E039/E320
Eq. (1) is invariant owing to its relation with an operator of
group G(K E) . After some manipulation and transformation, and
using an invariant sub-space Ln(K) , Eq. (1) becomes
equivalent in form to;
a;1V WCV = f.(K)C IL
(3)
Here, 4 and '~J have values from I to a , where a is the
sub-space dimension* By the action of operator A(g) of
group G(K0) , the following relations are obtained.-
e(K) = s(A_I(g)K)
a0) (K) = A,,,, (A (g)K)A.4,.J(g) (7)
from which is derived a value for the matrix a(K)~.
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On the question of ....
341e 9
S/139/ft/ooo/oo6/007/023
E039/E320
a (K) = -1 a -1 (11) .
)IV PV') I j I ii I (1k K) PIL ii
The action of the operator T. BT on vector K gives the
relation:
TkK BK_ (12).
It can be shown that the matrix PIN coincides with the
corresponding matrix for the sub-space L0the method of
n
calculating this matrix is given in an appendix). If the
series for aIN (K) can be effectively solved, the conditions
(7) and (11) allow the reduction of all analysis parameters to
a small number of independent parameters. It is possible in
such a manner to examine the dispersion law around any point
K0 of the Brillouin zones. Taking the analysis as far as the
second term:
Card 3/4

On the question of ....
' ' 34189
S/139/6i/ooo,ao6/OO7/O23
~EOWE320
W = a' + a i (K K + aij (K
11V g-J i 01 2 1" i - Koi )(K Koj) (13)
we obtain the same results for the dispersion law as previously
obtained by the use of the theory of second-order perturbations
There is I Soviet-bloc reference.
ASSOCIATION-. Si.birskiy fiziko-tekhnicheskiy inst1tut pri
Tomskom gosuniversitote imeni V.V. Kuybysheva
(Siberian Physicotechnical Institute of Tomsk
State University imeni V.V. Kuybyshev)
SUBMITTED: JanuaryllOj 1961
Card 4/4

37718
S/139/62/000/002/014/028
E073/F-435
LUTHUR: Xhaldyshev, V.A.
TITLE: The possible structure of the energy spectrum of
chalcopyrite-type crystals
PERIODICAL: Izvestiya vysshikh uchebnylch zavedeniy, Flzlka,
no.2, 1962, 98-103
TEXT: The possible type of dependence of the energy on th~ wave
vector in the neighbourhood of various points of the Brillouin e.
zone is investigated by,means of the method, proposed'in an earli r
paper of the author (Izv. VUZ, Fizika, no.6, 1961, 118-51),for .
investigating the spectra of t ary compounds with a chalcopyrite-
-0 IT
type lattice (spatial group D2d This method is based on
determining the energy.ispectrum for electrons and crystals from
the wave vectov, without using the perturbation theory, by
obtaining an approximate formula for the function CW- for the
entire Brillouin zone. - Relations governing dispersiZnfor
typical points of the Brillouin zone are given in the paper.
Irreducible matrices are given in the appendix for the individual
points.
Card 1/2
I.-.1.

S/139/62/000/002/014/028
The possible structure ... B073/L435
ASSOCIATION: Sibirskiy fiziko-tekhnicheskiy institut pri Tomskom 7'
(,osuniversitete,imeni V.V.Kuybysheva V
(Siberian Physicotechnical Institute of Tomsk
State University imeni V.V.Kuybyshev)
SUBMITTED: January 10, 1961

37719
s/i3g/62/000/002/015/028
E073/E435
AUTHORS.' Chaldyshev, V.A., Kudryavtseva, N.V.
TITLE: On the question of investigating the energy spectrunt
of electrons in crystals. II
PERIODICAL: Izvestiya vysshikh uchebnykh zavedeniy, F�zika,
no'.2, 1962, lo4-107
TEXT: The authors propose a new method for determining the
relationships between the parameters of the dispersion law,
dependent on the spatial symmetry of the crystal. As shown in a
previous paper (Izv. VTJZ, Fizika, no.06, 1961, 48) the
investigation of the character of the energy spectrum of
electrons in crystals around any point k0 of the Brillouin
zone reduces to the analysis of the equation
det [a 11V W - 8 11V E (k) T =0 U)
The functions (k) must satisfy
(k) All- (g)all, (A- (g)k)A- (g) (2)
V
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S/139/62/000/002/ol5/028
On the question of investigating ... E073/E435
which is a result of the spatial symmetry of the crystal,
and
a- IN (k) = P; a.. (T,-' k) P
The use of Eq.(2) and (3) assumes that Aj,.9 (g) and P,)V,
as well as the action of the operators A(g) and Tk on the
wave vector-are known. The Droblem of determining the matrices
Al"(S) of the irreducible representations of the group G. for'
different points ko of the Brillouin zone reduces to the
calculation of irreducible.weighted'represen'Lations for weights of
certain types, corresponding~'to a certain point group R.
ASSOCIATION: Sibirskiy fiziko-takhnicheskiy institut pri Tomskom
gosiiniversitete imeni V.V.Kuybysheva (Siberian
Physicotechnical Institute~of Tomsk State University
imeni V.V.Kuybyshev)
SUBMITTIDD i. April 20, 1961
Card 2/2

S/139/62/000/003/004/021
E039/E42o'
AUTHORS: Chaldyshev. V'.~~avlov, SPD*
TITLE: Structure of the electron energy spectrum in crystals
with a N&C1 lattice
PERIODICAL: Izvestiya vysshikh uchebnykh zavedeniy. Fizika,
no-3, 1962, 35-37
TEXT: The possible dispersion laws near to'different points in
the Brillouln zones are investigated. The dependence of EW
in a quadratic approximation in studied by means of the usual
method of perturbation theory of the second order, the-well-known
Rp method. Results are given for a number of points neglecting
the influence of spin-orbital interactions. One, two and three
dimensional cases are considered. The change in structure is
also investigated when the influence of spin-orbital
interaction is taken into account.
ASSOCIATION: Sibirskly fimiko-tokhnicheakiy inistitut pri Tomskom-
gosuniversitete imeni V.V.Kuybyaheva (Siberian Physico-
i
Technical Institute at Tomsk Stati University imeni I
V.V.Kuybyshev)
SUBMITTED: April 18, 1961
Card 1/1

S/139/62/000/003/016/021
E039/E460
AUTHORS: Kudryavtoeva, N.V.,
TITLE: On the investigation of the energy spectrum of
electrons in a crystal. III. Certain propertioar of
weighted representations
PERIODICAL: Izves~iya vysshikh uchabnykh zavedeniy. Fizika,
no.3, 1962-, 133-139
TEXT: Earlier part - Izv. VUZ. Fizika, no.2. 1962, 104.
Certain properties of the weighted representations which are
necessary for the investigation of the energy spectrum of
electrons in a crystal lattice are established. A series of
definitions and theorems are established by groitp theory methods-.
The concept of a weighted representation in introduced.
R is a symmetry point group with elements. r If tp each
I
element r of R there corresponds a linear operator T(r) then,:''
T(ri)T(ri) -- T(ri,rj)T(rirj)
where ";!(r.,r.) is a scalar function satisfying the functional
equation.
'(rlr2,r3)
(r1, r2r3) (r2, r3)
Card 1/2 (r1, r2) Y ......

S/139/62/000/003/ol6/021
On the investigation of the energy ... E039/E460
then this correspondence.is-called the weighted representation of*
the group R and the function q)(rirj) the weight. If Is
unity, then the system reduces to the normal representation.
A series of theorems of the prop~erties of
qj are developed
covering reducible and irreducible representations. The
properties of tables of the weights are discussed.
ASSOCIATION: Sibirskiy fiziko-tekhnicheakiy inatitut pri Tomakom
gosuniversitete imeni V.V.Kuybyaheva.
(Siberian Physicotechnical Institute at Tomsk State
University imeni V.V.Kuybyshtv)
SUBMITTED; April 20, 1961
Card 2/2

S/139/62/000/004 /008/018
9132/9435.
AUTHORS: Kudryavtsova, N.V., Chaldyshev, V.A.'.*
TITLE: On the question of the investigation of*th**enirgy
spectrum of electrons in a crystal. IV'
PERIODICAL: Izvestiya vysshikh uchebnykh "vedeniy. Fizika,
no.4,, 1962, 98-ic)6.
TEXT: Theorems have already; been developed (Izv.VUZ Fizika, no.2,
1962) related to weighted distribution6 in the 32 crystaliogra phic
point groups, Those crystal c 'lasso'a for'which weighting only of
the first order can be realized are distinguished. Tables or
second order weighting are developed and ahbwn to be largely-
equivalent. The elements of t6 group -R jthei crystal class)
can be divided into subgroups, each separate cyclic groups, the
elements of which commute among themselves. One element may
belong to several cycles. These are tabulitod. It has already
been showvi that for tables of weighting* of the first order a-
one-dimenslonal weighted representation exi*sts. One-dimensional
representations no longer exist for tables of the weightings of
the second order when theme lead to antisymmetric weightings.
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S/139/62/000/004/008/018
On the question of the investigation 9132/E435
The theory developed appears to be a mathematical analogy of the
geometrical theory of black and white and coloured groups
developed by-A.V.Shubnikov and N.V.Belov by more intuitive methods.
There are 5 tables.
':';.ASSOCIATIONs Sibirskiy fiziko-tekhnicheskiy institut pri Tomskom.
gosuniversitete imeni V,V,Kuybysheva (Siberian
Physicotechnical Institute at Tomsk University imeni
V.V.Kuybyshev)
SUBM17TED: April 20, 1961
Card 2/2

Vlei 62/004/012/018/052
BI 04YBI 02
AUTHORS: Karavayevq GO F., Kudryavtsevap 1'. V.9 and Chaldyshev, V. A.,
I-------------
TITLE: The structure of ths.eloctron energy spectrum In Th 3 P4- type
PERIODICAL: Fisika tYerdogV't01'&# To 4P no* 12p 19620 3471-3481
TEXT: The covariant representation of~the symmetry properties of Th P
3 4
type crystals according to Z.,Wigner (Grdup'theo'ry and its Applicatibn to
the quantum Mechanics of Atomic Spectra, Academy ?roast 1959).is applied
t6.studying the-effect-that spatial, symmetry and isotropyof Z So -type
.3 4
compounds exerts on the alictron'energy spectrum. -For the symmetry group
6
T of the lattice type investigated and with type Fv of the Brillouin'~
d
zone, the dispersion laws near.the symmetry points of the Brillouin zone,.
are derived in parametric form on the basis of solutions to the algebraic
equation -a Mc E(Z)c The method used was suggested by V. A*
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S/18IJ62/004/012/018/052
The structure of the electron B104/BI02
Chaldyshev (Izv. vuzov SSSR9 rizi.jx, no. 69 48t. 19611 no. 6t 939 1960).
The symmetry coefficients a determine the character of the dispersions
law in the neighborhood of the symmetry points. The matrices 9 -Ila 11
ILV
are calculated in quadratic approximation with respect to 91, using the
matrices of the irreducible representations D(g) of the unitary and
antiunitary operatione.g. The representations of-the matrices are giveno~.
There are 1 figure and 13 tables.
ASSOCIATION: Tomskiy gos. universitet in. V9 V* Kuybyshev& (Tomsk StaW
University imeni Yo Ve Kuybyshev)
SUBMITTED: July 6. 1962
Card 2/2

GRAIMSUT, V. A,; PAVWVp S.
Structmv of Ow electron, energy mmetrm In crystals vith a
ftol tm lattice# UT. we. uch. sav.; fis 3235-37 162.
iKM& 15: 10)
2. Sibirskly ftsiko-tekhoichankly Institut pri Tcmkm gosu-
daritTemm univorsitete Imeni V. V. *aybyebeva.
(Ructroup-Spectra) (Crystal lattices)

K=RrA,rISEVA.. N.'T.; CRiLDYSHU, V. A.
luctron Onergy Opectrm in crystals. hrt 3. So= properties
or lad ,---presentations. Isv. vyes uch, sav.; fis. 39133-139
0629 (HIM 15: 10)
1, Sibirsmy risiko-takhnichook iy InBUtut pri Tommkois gosudarst-
veimm mlversitete bj~ni V. V. Kuybyaheva.
(Crystallogmpby, Mathezatical)

MJDRYAVTSIVA, N.V.; CHAIDYSHEV, V.A.
Study of the energy spectra-of-electrons in a crystal. Part A+e
1xv.vy9.uch.zav*; fize no.4:98-106 162* (MIRA 15:9)
1, Sibirskiy fiziko-tekhnichookiy inatitut pri Tomakom
gosudaretvennom universitete imni V~V* Kik7byabeva.
(Electrons-Spectra) (Crystal inttues)

KARAVAYEV, G.F.; NMRUFTSEVA, N.V.; CRAWTSOV, V.A.
Structure of the atieiv, spectrumof electrons in the Th P type
crystals. Fix.tvartela 4 no.3.2t3471-3481 D 162. A41533-2)
1. Tomskly gosudaretv universitst in. T. V.Ibyshan,
(Groups, Theory of (Ilectron"pectria
(crystal lattices)

TWO V.A.; KMRTAVTSEVAq N.V.; KWVAYEV, G.F.
energy 9powbm in crystaU, Part 5t.L.oaded corepresentations,
;STG*GWh9b.Wr.;fit*no.2t4&52 103.
(KMA 16;5)
I* SibdLrokly fisik6-tekhulchookly instutut pri Tomakcis goeudirstvennas
gAi*ersitete 4mmi V.V*ukrsheva.
(Cr7#tallOgrapb.*p'Mav,hmatical) (Mmtrone-apectra)

CHALDYSHZVg V.A.; KAUVAYEV, G.F.
Valence band Siructure of chalcopyrite type compounds. Izv. vyS.
ucheb. says; f#* nc,5t103-112 63. (MRA 16:U)
1. 6ibirskiy fiaiko-tekbnicheskiy institut pri Tomskom gasudarst-
vennom universitete imeni Kuybysheva,

CPIAMYSITEV, V.A.; Kfr-,A'IAYEV, G.F.
UT-octure of the energy spectrum c, cbAI-opyr,'te type crystals.
Izv. vys. ucheb. zav.; fiz. no. 2;28~30 (M 1 RA 17 -. 6
1. Sibirskily fiziko-tekhnicheskiy inst-Atilt pri Toinskom
gosudar-Mennom universite-te iiiiani V.V.Kiiybyshev&.

h'ORYAVTSEVA$ N.V.; ~.V.A.
Studying the energy spectrum of electrons in crystals. Part 7. Izv.
vys. ucheb. zav.; fiz. 8 no.3:105-111 165. (,kmk 18:9)
1. Sibirskiy fiziko-tekhnicheskiy institut imeni V.D.Kuzret'.qova.

L 09237-67 MM IJP(a)
SOURCE CODE: UR/0l39/66/000/60Q6i61F/6i00F
AUTHOR: Wdryavtsovas No V. Chaldyshovp Ve A.
ORG; Siborlan PhysicotachnIcal Institut Ime V. D. 13uznatsov (Sibirskly f Isikow
tQ1dulichaskly lnstituO
TIM: Investigation of the oncray si)ectra of oloctK2n In a crystal* Me
Wfif -group
Characteristics of loaded corepresontations of po a [Whs Dwt--D6h
WbkM: !A2. Mika, no. 4. 1066, 108-109
TOPIC TAGS., electron spectrums crystallography
ABSTILACT: Characteristics are given for Irreducible nonequivalent loaded core-
presentations of all possible types of coequivalent loads for the groups D2h, D4h,
'and D6h, which can have seven types of equivalent loads of the second order. Results
are given in an extensive table, which Is explained in detail@ Origs arte hasg
1 table. LJ-PRS: 30,040]
SUB CODE: 20 SUBM DATEs 23)br65 VORIG REFt 007-
,~Card- 1/3LV~~

CHALSORI, Jamass, agr ins.
-------------
Inf3pence of the positi!pn of the ctic point of the telescope
of the automatic 16TW43V ins cc the leveling error of the
aim axis. Przagl Va# ~5 no.M.159-160 Ap 163.

CHAIECKI., Janusz., mgr inz.
Prism compensator of the sight line inclination in a level.
Frzogl good 35 ji.e.361 no. N104-106 * 164.

COU1.4TRY --,c 1 it nd
Foresixy. Forest. Mhnaf~wnent.
ABS . JOUR. RZhBiol-, LNO- - 14 19-5a, -'40- 632U
AUT-ion Chalecki, Loon
T: The Cc-rcept of Closure Is lot Nyorthless
0 PU-' L,is nolski, 1957, 11, No. 17, 10-12
a four-noint scale
Un to the Dresent time in ?oltna
,
is aw3loyed to determtne cro,4n closure, according to
which "he latzer my lbe "total", "Inter-neliate",
"discontAntiour." ani "sparne stand ". 'he quthor
recommends chani7ing to the universn'Lly-adout-ed ten-
point scale, since this better fulfills che recuirements
of' rational forest management.
CA3D: 1/1

CULECKI, L.
Forest roads an dividing lines. v. 6.
IAS POIASKI. (Ministerstwo Lesnictum araz Stammyg2enie Naukowo-Techniesne
Inzynierow i Technikow Lesnictwa i Drzewnictua) Warazava, Poland. Vol. 32,
no. 12, June 1958.
Monthly List of East European Accession (EEAI) LC, Vol. 9, no. 1, Jan. 1960.
Uncl.

CHALECKI, L.
Alter-nation of stand to be cropped. p. 39
SYLUAN (Wydzial Nauk 11olniczych i Lemych Folskiej Akademii Nauk i Polskie
Towarzystwo Lesne) Warszawa, Poland. Vol. 103, no. 3, mar 1959
Monthly List of East European Accessions (EEAI) 141, Vol, 80 no. 9, September 1959.
Uncl.

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"Raw Material for Cider Production in Gelendshik District.9" Vin SSSR 12, No 8,
1952.
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