Рубин А.Б.Лекции по биофизике

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djb\hc b aZ ± fk \uo h^bl gZ ihklhygguc mjh\_gv <hkklZgh\e_gb_

gZljb_\hc ijh\h^bfhklb ^h bkoh^guo agZq_gb c  i jhbkoh^bl \  jZa

[uklj__ q_f dZeb_\hc ijh\h^bfhklb <hijhk h lhf dZdbf h[jZahf

ijh\h^bfhk lvbhgguodZgZeh\mijZ\ey_lky we_dl jbq_kdb f ihe_f y\ey

_lkyh^gbfbap_gljZevguo\[bhnbabd_f_f[jZgguo ijhp_kkh\ < fh

^_eb Oh^`dbgZ±OZdkeb ij_^iheZ]Z_lky qlh ijh\h^bf hklv ^ey bhgh\

1D b D j_]mebjm_lky g_dhlhjufb i heh`bl_evgh aZjy`_ggufb mijZ\

eyxsbfbqZklbpZf b dhlhju_i_j_f_sZxlky \ f_f[jZg_ijbbaf_g_gb

yow e_dl jbq_kdh]hihey Kf_s_gb_ iheh`_gby wlbo qZklbp  \ f_f[jZg_

aZ\bkbl hl ijbeh`_ggh]h ihl_gpbZeZ b khhl\_lkl\mxsbf h[jZahf hl

dju\Z_lbebaZdju\Z_lbhgguc dZgZeKqblZ_lkyqlh \kemqZ_dZeb_\hc

ijh\h^bfhklbbf_xlkyq_luj_Zd l b\bjmxsb _ dZgZevgmxijh\h^bfhklv

qZklbpu<kemqZ_1D±dZgZeZij_^iheZ]Z_lkygZebqb_  lj_oZdlb\bjmx

sbo qZklbp g_h[oh^bfuo ^ey hldju\Zgby b h^ghc bgZdlb\bjmxs_c

qZklbpu±^ey aZdju\Zgby dZgZeZ GZ hk gh\_ wlbo ij_^iheh`_gbc m^Z

ehkvihkljhblvfZl_fZlbq_kdmxfh^_evk\ukhdhclhqghklvx \hkijhba

\h^ysmx g_j\guc bfimevk =eZ\gh_ ^hklb`_gb_ khklhbl \ jZa^_e_gbb

ljZgkf_f [jZgguolhdh\gZhl^_evgu_dhfihg_gluL

1D

bL

 b\wdki_jb

f_glZevghf bamq_gbb bo k\hckl\ < nmgdpbhgZevghc kljmd l mj_ dZgZeZ

[ueb\u^_e_guwe_f _g luhl\_lkl\_ggu_aZf_oZgbafuk_e_dp b bbhgh\

k_e_dlb \guc nbevlj Zdlb\ZpbbZdlb\Zpbhggu_ \hjhlZ b bgZdlb\Z

pbbdZgZeZbgZdlb\Zpbhggu_\hjhlZjbk>\b`_gb_aZjy`_gguo

mijZ\eyxs boqZklbp\dZgZe_\hjhlg uoqZklbph[gZjm`b\Z_lkywdki_

jbf_glZevghih\hagbdgh\_gbx\hjhlguo lhdh\ Hgb ihy\eyxlky \ j_

amevlZl_ kf_s_gby qZklbp \ f_f[jZg_ ih^ \ebygb_f gZeh`_ggh]h gZ

f_f[jZgmwe_dljbq_kdh]hbfimevkZM^Zehkvh[gZjm`blv \hjhlgu_lhdb

kf_s_g b y k\yaZggu_ k qZklbpZf b  hl ju\Zxsbfb1DdZgZe <f_kl_ k

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l_fij_^iheh`_gb_qlhi _j_kdhdg_kd hevdboaZjy`_gguo]jm ii^he`_g

ijhbkoh^blv q_j_a \kx lhesm f_f[jZgu i j_^klZ\ey_lky fZeh\_jhyl

guf Ihwlhfm \u^\b]Z_lky ^jm]Zy bgl_jij_lZpby ijbjh^u \hjhlguo

lhdh\ Ij_^iheZ]Z_lky qlh lhdb kf_s_gby h[mkeh\e_g u g_ l jZgkf _f

[jZgguf i_j_k dhdhfaZjy`_gguoqZklbp  Zd hhi_jZlb\gufbaf_g_gb_f

hjb_glZpbb^bihe_c\uklbeZxsbo \gmlj_ggxxihehklvdZgZeZ

Iheyjgu_]jmiiuhij_^_eyxsb_^bihevgh_hdjm`_gb_bhgZ\dZgZ

e_\ebyxlgZwg_j]bxbhgZbgZijhoh`^_gb__]hq_j_adZgZe?kebih^

\ebygb_f ^_iheyjbamxs_]h we_dljbq_kdh]h bfimevkZ baf_gy_lky bo

hjb_glZpby lh wlh \uah\_l kf_s_gb _ aZjy`_gguo ]jmii b baf_g_gb_

ijh\h^bfhklb dZgZeZ Ijhp_kk i_j_hjb_glZpbb ^bihe_c fh`_l ghkblv

dhhi_jZlb\gucoZjZdl_jb[ulv^hklZlhqghj_adbf <wlhfkemqZ_wg_j

]by g_h[oh^bfZy ^ey i_j_hjb_glZpbb dZ`^h]h we_f_g lZjg h]h ^bihey

^he`gZ aZ\bk_lv g_ lhevdh hl _]h kh[kl\_gghc wg_j]bb gh b hl ^heb

^bihe_c m`_ baf_gb\rbo k\hx hjb_glZpbx Bgufb keh\Zfb ih f_j_

baf_g_gby hjb_ glZpbb qZklb  ^bihe_c wg_j]by g_h[oh^bfZy ^ey i_j_

hjb_glZpbb hklZ\rb oky ^bihe_c mf_gvrZ_l ky l_f ag Zqb l_evg__ q_f

[hevr_ qbkeh m`_ i_j_hjb_glbjh\Zgguo ^bihe_c Fh`gh ij_^klZ\blv

JbkKljh_gb_bhggh]hdZgZeZihObee



k_[_qlh \bkoh^ghf khklhygbb ^bihebf_rZxl ^jm] ^jm]m  baf_gblv

hjb_glZpbx ih^ ^_ckl\b_f ihey Z i_j_hjb_glbjh\Zggu_ ^biheb m`_

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jZlb\gh]hwnn_dlZijh\h^bfhk lvdZgZeZhq_ gv[ukljheZ \bg hh[jZagh

gZjZklZ_lih^ ^_ckl\b_fijbeh`_ggh]h w e_dl jbq_kdh]hbfimevkZAZf _

lbfqlhbdhgnhjfZpbhggu_i _j_kljhcdb\ dZgZe_khijh\h`^Zxsb _ k y

ih\hjhlhf ^bihe_cfh]ml lZd`_ ijb\h^blv d kdZqdhh[jZaguf baf_g_

gbyf ijh\h^bfhklb \ h^bghqghf dZgZe_ NZd lb q_kdb  \h \k_o ij_^eh

`_gguofh^_eyoj_qvb^_lhk\h_]hjh^ZnZah\uoi_j_oh^Zo\f_f[jZgZo

e_`Zsb o \ hkgh\_ kdZqdhh[jZaguo i_j_oh^h\ dZgZeZ f_`^m ^\mfy kh

klhygbyfb

JZ kijhkljZg_gb_ g_j\gh]h bfimevkZ\^hev\hehdgZ ijhbkoh^bl

[_a aZlmoZgby k ihklhygghc kdhjhklvx <gmlj_ggyy qZklv \hehdgZ gZ

mqZkld _ \hagbdgh\_gby kiZcd Z aZjy`_gZ iheh`bl_evgh Z \ khk_^gbo

ihdhysbokymqZkldZo±hljbpZl_evghjbk  <ke_^kl\ b_ wlh]h \ha

gbdZ_lehdZevguc lhd f_`^m \ha[m`^_gguf b ihdhysbfky mqZkldZf b 

GZijZ\e_gb__]h lZdh\h qlh hg  ^_iheyjbam_l h[eZklv f_f[jZgu i_j_^

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\_gbx\g_ckiZcdZ LZdbfh[jZahf \ha[m`^_gb_i _j_^Z_lky^Zevr_ih

\hehdgm G_j\gh_ \hehdgh fh`gh mih^h[blv w e_dl jbq_kdhf m dZ[_ex

khk_^gb_mqZkldb dhlhjh]h k\yaZgu f_`^m kh[hc H^gZdh \ hlebqb_ hl

h[uqgh]h dZ[_ey jZkijhkljZg_gb _ g_j\gh]h bfimevkZ khijh\h`^Z_lky

_]h aZlmoZgb_f ihkdhevdm \ f_f[jZg_ bf_xlky fhe_dmeyjgu_

]_g_jZlhjuih^iblu\Zxsb_ [_]msbc bfimevk GZoh`^_gb_ kdhjhklb

jZkijhkljZg_gby g_j\gh]h bfimevkZ lj_[m_l



bkke_^h\Zgby dbg_lbdb

bhgguo l jZgkf_f[jZgguo lhdh\L

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 L

 lhdZ ml_qdb Z  lZd`_ agZgby

we_dljb q_kdb o k\hckl\ g_j\gh]h \hehdgZ_fdhklv b  khijhlb\e_gb_

:gZebakhhl\_lkl\mxsbofZl_fZlbq_kdbofh^_e_cihdZau\Z_lqlhkdh

jhklvjZkijhkljZg_gb ymklhcqb\h]h bfimevkZ h[jZlghijhihjpbhgZevgZ

d\Z^jZlghfm dhjgx ba ^bZf_ljZ \hehdgZ qlh kh\iZ^Z_l k wdki_jbf_g 

JbkAZjy`_gb_ih\_joghklbg_j\gh]h\hehdgZijbjZkijh

kljZg_gbbbfimevkZBeexkljZpbyl_hjbbehdZevguolhdh\ih

Oh^`dbg



lZevgufb^Zggufb < hj]Zgbaf_ g_j\gu_ \hehdgZ h[t_^bg_gu \ g_j\

gu_kl \heu ]^_ dZ`^h_ \hehdgh fh`_l kZfhklhyl_evgh ijh\h^blv \ha

[m`^_gb_We_dljbq_kdh_ ihe_ \hagbdZxs__ijbwlhf\ \ha[m`^_gghf

\hehdg_ \eby_l gZ f_f[jZgguc ihl_gpbZe khk_^gbo \hehdhg dhlhju_

l_fkZfufijbg_dhlhjuomkeh\byofh]mllZd`_



\ha[m`^Zlvky



E_dpbyI?J<BQGU?

IJHP?KKULJ:GKNHJF:PBB

WG?J=BB<NHLHKBGL?A?

Ihke_^h\Zl_evghklvhl^_evg uoj_Zdpbc\nhlh[bheh]bq_kdboijh

p_kkZo \dexqZ_l dZd ijZ\beh ke_^mxsb _ klZ^bb ih]ehs_gb_ d\ZglZ

k\_lZ ojhfhnhjghc ]jmiihc b h[jZah\Zgb_ we_dljhggh\ha[m`^_gguo

khklhygbc o fb]jZpby wg_j]bb we_dljhggh]h \ha[m`^_gby o i_j\bq

guc nhlhnbabq_kdbc Zdl b

ihy\e_gb_i_j\bqguo nhlh

ijh^mdlh\ o h[jZah\Zgb_

i_j\bqguo klZ[bevguo ob

fbq_kdb o kh_^bg_gbc o

nbabheh]h[bhobfbq_kdb_

ijhp_kku o dhg_qguc nh

lh[bheh]bq_kdbcwnn_dl

< aZ^Zqm [bhnbabdb

\o h^bl \uykg_gb_ f_oZgba

fh\ gZqZevguo klZ^bc dh

lhju_ ke_^mxl

g_ihkj_^kl\_ggh aZ ih]eh

s_gb_f d\ZglZ k\_lZ DZd

fu m\b^bf g_k fhljy gZ

[hevrh_ jZaghh[jZab_  nh

lh[bheh]bq_kdbo wnn_dlh\

bf_ggh gZqZevgu_ wlZiu

ij_h[jZah\Zgby wg_j]bb

k\_lZ oZjZdl_jbamxlky h[

sbfb fhe_d meyjgufbf_oZ

gbafZfb < hkgh\_

i_j\bqguo ijhp_kkh\ nhlh

kbgl_aZ e_`bl keh`gZy

kh\hdmi g hklvhdb k ebl_evgh

\hkklZgh\bl_evguo j_Zdpb c

i_j_ghkZ we_dljhgZ  \ we_d

ljhg ljZkihjlghc p_ib

WLP

H[s Zy ko_fZ GZjbk

 ijb\_^_gZ h[s_ijbgy

lZy=±F[HfZ i_j\bqguo

klZ^bc nhlhkbgl_aZ \ukrbo

JbkKo _fZi_j\bqguo ijh

p_kkh\ nhlhkbgl_aZ \ukr bo jZkl_gb c 

< khhl\_lkl\bb k i j_^klZ\e_gbyfb h

ihke_^h\Zl_evghf \aZbfh^_ckl\bb

^\monhlhkbkl_f  \lZdgZau\Z_fhc=±

ko_f_ nhlhkbgl_aZ \hkklZgh\e_ggu_

ijh^mdluNK,,kem`Zl^hghjZf bwe_d

ljhg h\^eyNK<ha[m`^_gb_k\_lhf

dhl hjuc \ hk gh\ghf  i h]ehsZ_lky NK

,, ^he`gh ijb\h^blv d \hkklZgh\e_

gbx ijhf_`mlhqguo i_j_ghkqbdh\ \

WLPZ\ha[m`^_gb_NKgZh[hjhl  d

bohdbke_gbx



jZkl_gbc  ]^_mdZaZgulZd`_\j_f_gZi_j_ghkZwe_dljhgZgZ hl^_evguo

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