NbabdZ de Mq [ eyh[s h[jZah\Zlmq [aZ\ gbcª

^\b`mlkywe_dljhgufZkkZdhlhjuofgh]hf_gvr_fZkkuy^jZ

4.

Kh]eZkgh y^_jghc fh^_eb \ p_glj_ ZlhfZ gZoh^blky

iheh`bl_evgh aZjy`_ggh_ y^jh 

fZkkZdhlhjuofgh]hf_gvr_fZkkuy^jZ

5.

?keb

α

qZklbpZ ijhe_lZ_l hq_gv [ebadh d y^jm lh hgZ kbevgh

hldehgy_lky

hl

i_j\hgZqZevgh]h

gZijZ\e_gby

^\b`_gby

dmehgh\kdhckbehcLdjZaf_juy^jZhq_gvfZeuih kjZ\g_gbx k

jZaf_jZfbZlhfZlhhkgh\gZyqZklv

α

qZklbpijhe_lZ_l^hklZlhqgh

^Ze_dhhly^jZb g_bkiulu\Z_lkbevgh]hhldehg_gby

§57.

1.

JZ^bcij_\jZsZ_lky\ jZ^hg

2.

Ijhbkoh^blij_\jZs_gb_h^gh]hobfbq_kdh]hwe_f_glZ\ ^jm]hc

3.

Y^jh

4.

He

Rn

Rd

4

2

222

86

226

88

+

→

 ]^_ He

4

2

 —

α

qZklbpZ

Rd

226

88

² y^jh

jZ^by

Rn

222

86

²y^jhjZ^hgZ

5.

<_jog__qbkeh²fZkkh\h_qbkehgb`g__²aZjy^h\h_qbkeh

6.

FZkkh\h_qbkehy^jZZlhfZ^Zggh]hobfbq_kdh]hwe_f_glZjZ\gh

k lhqghklvx^hp_euoqbkemZlhfguo_^bgbpfZkkukh^_j`Zsboky

\ fZkk_ wlh]h y^jZ AZjy^h\h_ qbkeh y^jZ ZlhfZ ^Zggh]h

obfbq_kdh]h we_f_glZ jZ\gh aZjy^m y^jZ \ujZ`_gghfm \

we_f_glZjguowe_dljbq_kdboaZjy^Zo

7.

He

Rn

Rd

4

2

222

86

226

88

+

→

Ba^Zgghcj_Zdpbb\b^ghqlh\uihegyxlky

aZdhgu khojZg_gby fZkkh\h]h qbkeZ b aZjy^Z >_ckl\bl_evgh

fZkkh\h_qbkeh  b aZjy^  jZkiZ^Zxs_]hkyy^jZZlhfZjZ^by

jZ\gu khhl\_lkl\_ggh kmff_ fZkkh\uo qbk_e         b

kmff_ aZjy^h\         h[jZah\Z\rboky \ j_amevlZl_ jZkiZ^Z

Zlhfh\jZ^hgZb ]_eby

8.

Y^jZZlhfh\bf__lkeh`gh_kljh_gb_

9.

JZ^bhZdlb\ghklvxgZau\Zxlkihkh[ghklvy^_jZlhfh\g_dhlhjuo

obfbq_kdbo we_f_glh\ kZfhijhba\hevgh ij_\jZsZlvky \ ^jm]b_

y^jZk bkimkdZgb_fqZklbp

31

§58.

1.

Kq_lqbd =_c]_jZ khklhbl ba ]_jf_lbqghc kl_deygghc ljm[db

aZiheg_gghc jZaj_`_gguf ]Zahf gZijbf_j Zj]hghf < g__ \iZygu

we_dljh^u  dZlh^ b Zgh^  ih^dexq_ggu_ q_j_a khijhlb\e_gb_ R d

bklhqgbdm \ukhdh]h gZijy`_gby Ijbgpbi kq_lqbdZ =_c]_jZ

ke_^mxsbc Ijb ijhe_l_ \gmljb ljm[db dZdhcgb[m^v [ukljhc

qZklbpu kihkh[ghc bhgbabjh\Zlv Zlhfu ]ZaZ h[jZam_lky g_dhlhjh_

qbkehwe_dljhgbhgguoiZjWe_dljhgugZqbgZxl^\b]Zlvkyd Zgh^mZ

iheh`bl_evgu_ bhgu ² d dZlh^m ?keb gZijy`_gghklv ihey

^hklZlhqgh\_ebdZlhwe_dljhgmkdhjyykvfh`_lijbh[j_klbwg_j]bx

^hklZlhqgmx ^ey bhgbaZpbb Zlhfh\ ]ZaZ 

we_dljhgumkdhjyxlkyihe_fb \k\hxhq_j_^vijhba\h^ylbhgbaZpbx

^Z\Zy gZqZeZ gh\uf we_dljhgZf b bhgZf < ljm[d_ h[jZam_lky lZd

gZau\Z_fZy we_dljhgghbhggZy eZ\bgZ < j_amevlZl_ wlh]h \ ljm[d_

\hagbdZ_l jZajy^ b \ p_ib kq_lqbdZ ijhbkoh^bl djZldh\j_f_ggh_ b

j_adh_ \hajZklZgb_ kbeu lhdZ dhlhjh_ j_]bkljbjm_lky ki_pbZevguf

mkljhckl\hf JZajy^ ^eblky ijbf_jgh fbdjhk_dmg^m b aZl_f

ij_djZsZ_lky ld hkgh\gZy qZklv gZijy`_gby iZ^Z_l gZ

khijhlb\e_gbb R b \ j_amevlZl_ wlh]h gZijy`_gb_ f_`^m dZlh^hf b

Zgh^hfj_adhmf_gvrZ_lky

2.

>eyj_]bkljZpbbwe_dljhgh\b

γ

d\Zglh\

3.

DZf_jZ 

djurdhcLLPGZ

^g_ dZf_ju e_`bl q_jgZy ijhiblZggZy kf_kvx \h^u kh kibjlhf

ldZgv FF [eZ]h^Zjy dhlhjhc \ dZf_j_ \ha^mo gZkus_g < dZf_j_

hlkmlkl\mxl y^jZ dhg^_gkZpbb Ijbgpbi ^_ckl\by dZf_ju

l_fi_jZlmjZ \ g_c iZ^Z_l b iZju \gmljb klZgh\ylky

i_j_kus_ggufb l_ hgb l_i_jv fh]ml e_]dh dhg^_gkbjh\Zlvky gZ

y^jZo dhg^_gkZpbb gZijbf_j gZ bhgZo Q_j_a lhgdh_ hdhrdh

dZf_ju \imkdZ_lky imqhd bkke_^m_fuo qZklbp dhlhjuc ijhe_lZy

q_j_a ]Za kha^Z_l gZ k\h_f imlb bhgu  y^jZ dhg^_gkZpbb  IZju

dhg^_gkbjmxlky gZ bhgZo b \ blh]_ \^hev ljZ_dlhjbb ^\b`_gby

qZklbpu h[jZam_lky \b^bfuc ke_^ ba dZi_e_d iZjZ  lj_d  LZdbf

h[jZahf k ihfhsvx dZf_ju 

ljZ_dlhjbx^\b`_gbyqZklbpu

4.

?kebdZf_jm

ljZ_dlhjbx ^\b`_gby qZklbpu fu fh`_f hij_^_eblv agZd aZjy^Z

qZklbpu  ih gZijZ\e_gbx ba]b[Z  __ fZkkm wg_j]bx aZjy^  ih

jZ^bmkmdjb\baguljZ_dlhjbb 

32

5.

Imaujvdh\Zy dZf_jZ h[eZ^Z_l [hevrbf [ukljh^_ckl\b_f \

hlebqb_ hl dZf_ju 

dZf_ju 

ijbf_gy_lkyi_j_]j_lZy\ur_lhqdbdbi_gby`b^dhklv

§59.

1.

Hiul aZdexqZ_lky \ bkke_^h\Zgbb \aZbfh^_ckl\by

α

qZklbp k

y^jZfbZlhfh\ZahlZE_lysZyk [hevrhckdhjhklvx

α

qZklbpZijb

ihiZ^Zgbb \ y^jh ZlhfZ ZahlZ \u[b\ZeZ ba g_]h y^jh ZlhfZ

\h^hjh^Zdhlhjh_J_a_jnhj^gZa\Zeijhlhghf

2.

H lhfqlh\ j_amevlZl_\aZbfh^_ckl\by

α

qZklbpk y^jZfbZlhfh\

ZahlZh[jZah\Zebkvy^jZdbkehjh^Zb \h^hjh^Z

3.

Y^jh ZlhfZ \h^hjh^Z G

1

1

bgZq_ gZau\Z_lky ijhlhghf b

h[hagZqZ_lkykbf\hehf p

1

1

bebp.

4.

Ij_^iheh`_gb_h lhfqlhijhlhgu\oh^yl\ khklZ\y^jZex[h]h

ZlhfZ

§60.

1.

Y^jZZlhfh\bf_xl[hevrmxfZkkmq_fkmfZfZkkkhklZ\eyxsbo

boijhlhgh\Wlh[uehmklZgh\e_ghhiulgufiml_fb ^Z_liheZ]Zlv

qlhihfbfhijhlhgh\\ khklZ\y^jZ\oh^yldZdb_lh^jm]b_qZklbpu

2.

Wlhij_^iheh`_gb_[ueh\ukdZaZghWjg_klhfJ_a_jnhj^hf\ ]

3.

>`_cfkQ_^\bd\ ]

4.

M g_cljhgh\ hlkmlkl\m_l aZjy^ ihkdhevdm hg g_ hldehgy_lky

we_dljbq_kdbf b fZ]gblguf ihe_f FZkkm hij_^_ebeb ba

dhebq_kl\_gguo oZjZdl_jbklbd \aZbfh^_ckl\by g_cljhgZ k ^jm]bfb

qZklbpZfb

5.

G_cljhgh[hagZqZ_lkykbf\hehf n

1

0

bebn_]hfZkkZihqlbjZ\gZ

g_fgh]h[hevr_ fZkk_ijhlhgZ

§61.

1.

Gmdehgu

2.

FZkkh\uf qbkehf gZau\Z_lky qbkeh gmdehgh\ \ y^j_ ZlhfZ

FZkkh\h_qbkehh[hagZqZ_lky[md\hc:.

3.

FZkkh\h_ qbkeh jZ\gh k lhqghklvx ^h p_euo qbkem Zlhfguo

_^bgbpfZkkukh^_j`Zsboky\ fZkk_ZlhfZ

4.

Qbkeh ijhlhgh\ \ Zlhf_ h[hagZqZ_lky [md\hc Z b gZau\Z_lky

aZjy^h\ufqbkehf

5.

I_j_^kbf\hehfkgbam

33

6.

AZjy^h\h_qbkehjZ\ghaZjy^my^jZ\ujZ`_gghfm\ we_f_glZjguo

we_dljbq_kdbo aZjy^Zo AZjy^h\h_ qbkeh ZlhfZ jZ\gh _]h

ihjy^dh\hfmghf_jm\ lZ[ebp_F_g^_e__\Z

7.

X

A

Z

a^_kvO ²kbf\heobfbq_kdh]hwe_f_glZ

8.

Qbkehg_cljhgh\\ y^j_h[hagZqZxl[md\hcN.

9. A = Z + N.

§62.

1.

Bahlhiu ² we_f_glu k h^bgZdh\ufb aZjy^Zfb y^_j gh

jZaebqgufbfZkkZfb

2.

Y^jZbahlhih\h^gh]hwe_f_glZbf_xlh^bgZdh\ucaZjy^

3.

JZagu_ bahlhiu h^gh]h we_f_glZ kh^_j`Zl jZagh_ dhebq_kl\h

g_cljhgh\

4.

M \h^hjh^Z _klv ljb bahlhiZ ijhlbc   G

1

1

 ^_cl_jbc   G

2

1

),

ljblbc  G

3

1

).

5.

IhlhfmqlhfZkkZZlhfh\\uqbkey_lkydZdkj_^g__agZq_gb_fZkk

\k_o_]hbahlhih\

§63.

1.

FZkkZZlhfZmf_gvrZ_lkygZZ aZjy^_]hy^jZ²gZ

2.

GZijbf_j

He

Rn

Rd

4

2

222

86

226

88

+

→

.

3.

Y^jhjZ^hgZkh^_j`blgZijhlhgZf_gvr_q_fy^jhjZ^by

4.

Ijb

α

jZkiZ^_ h[jZam_lky gh\uc obfbq_kdbc we_f_gl

ihjy^dh\uc ghf_j dhlhjh]h \ lZ[ebp_ F_g^_e__\Z f_gvr_

bkoh^gh]hgZ

5.

Ijb

β

jZkiZ^_ baemqZ_lky we_dljhg b Zglbg_cljbgh H^bg

g_cljhg\ y^j_ijblZdhfjZkiZ^_ij_\jZsZ_lky\ ijhlhgwe_dljhg

b Zglbg_cljbgh

6.

Ijb

β

jZkiZ^_ h[jZam_lky gh\uc obfbq_kdbc we_f_gl

ihjy^dh\uc ghf_j dhlhjh]h \ lZ[ebp_ F_g^_e__\Z [hevr_

bkoh^gh]hgZ

7.

G_l ihlhfm qlh fZkkh\h_ qbkeh jZ\gh qbkem gmdehgh\ Z wlh

qbkehijb

β

jZkiZ^_g_f_gy_lky

8.

>ey

α

jZkiZ^Z

He

Y

X

4

2

4

2

+

→

−

−

A

Z

A

Z

.

>ey

β

jZkiZ^Z

~

Y

X

0

0

0

1

1

+

+

→

−

+

e

A

Z

A

Z

.

9.

α

b

β

jZkiZ^qZklhkhijh\h`^Z_lky

γ

baemq_gb_f

34

§64.

1.