ä

T 3 R = K

ft mv = π R πr T = R v f = mv R 1 R R [8] F F / m t R v 1 F R 1 = R m v mv F = R

BE BA = BA BD DE DA = DA DB DB ADEA = DE 1 f R = m T 4π mr f = T R f T T = π R v f = v R v πr π R R v

f = R 3 R 1 = T T R R 1 f R h = π R 19.7393 60 3500 5000 = T ( 7. 316) ( 4) ( 60)

136. 1 16 ( 60) 4300 h = = π R π 60 19615800 T ( 39343) 15.009 15 1 1 15 1 1

t = π L g v F R

= 1 a α = v R

1 1 AF AE = FC DC AE = FC CD FA EM ( AE) = DN ( CD) EM ( FC) = DN ( FA)

FA FC = ( ) F ( FA) C F f P P pf = ( ) ( PF)

PI PS S PQ PS pi ps ( ( PF pq pf F f P P PF pf ps pf PF PS ( ps) = = PS ps ( PS)

m m F F G m m 1 1 = R R

m g = G m m 1 1 r G = r m 1/ g G g

FdS = 1 mv

1 3 1 1.84 73 J = A Q = 3.65J /

1 mv 1 mv m R v Fdr r 1 mv - 1 R mv = - Fdr r

A A' η = ' η = Q Q'

A A η = η = ' Q Q' 1 1 A A', ',, Q Q' 1 1

u cosθ h πr sinθrdθ hr = sinθdθ Nu h cos θ sin θ d θ π/ Nu F = ( mu cos θ) cosθ sinθdθ 0 h Nmu = 3h F Nmu p = = a 3V 1 p = nmu 3 3p 1 = nmu

1 nmu = T ρ, = nmg u = 3p nm = 3pg ρ

πρ δ λ λ W δ = 1 πρ λ δ ( ) 3 α = πρ 3 λ 3 ( πρ / λ ) πρ e dx 3 λ 3 1 3 πρ λ πρ ( / ) x L' = Ne xdx N 0 3 λ 3 λ = πρ N V = V 3 N V L'= n πρ n = N V L' = 1 n πρ

3 4 u L = 3 1 4 nπρ

A, - 1, X X + dx a NCe -(x /a ) dx

+ NCe ( x / a ) dx = N NC πa = N 1 C = a π 1 e ( x / a ) a π 1 x a N e ( / ) dx a π 1 ( v / a ) N u e dv a 3 π = a π 3 v = a

ϕ ϕ

β C e 1 ( ξ + η + ζ )/ a dξdηdζ N a dn1 = e d d d 3 3 ( ξ + η + ζ )/ ξ η ζ / α π

dq : T

dq T dq T = 0 < 0 [3] dq ds = T ( ) ( 1) ds = S S 1 dq mationconcent T

( ) dq ( 1) dq + < T 0 ( 1) r ( ) T r ( 1) dq = S1 S r( ) T ( ) dq < S S1 ( 1) T

t F' = F t' F' d = F d' B = K I r

db K Ids sinθ = r db K Ids = r r θ= aιdssinθ a B K K Id θ = = θ= 0 r 0 r a I sinθ KI a = K d = 0 dsinα θ dsin α ( cos θ ) 0 KI KI = 1 = d sin ( cos ) d tg α α α α tg α Ftg - a = 45 α ο Ftg = Ftg 30' = 0. 41414F K t' K ( K t t ' )( t + t ') = t t t' O K V,

O V = ( t t 0')( t + t' 0 ) t' V ( t t ')( t + t' ) t' V V 0 1 d d + 9 d 1 + 9 9, d d 9 9 d 1+ d 1 = + d d F0 9 O 1 + F d V v 1 F F 0 v O 1 = V 9 1 + d α 0.87545 0.8847 Ftg

ii'dsds' sinθsin θ'cosϖ r n Kii' dsds'cos θcosθ' r n ii ' dsds ' (sin K n θ sin θ ' cos ω + cos θ cos θ ') r n = K = - 1 Tricker ii' dsds' 1 F = r sinθ sin θ'cosϖ cosθcos θ' ii' ds' cos θ df = sin θ ds r ii' ds' cos θ df = sin θ ds r r = d θ r d = -sinθ sinθ ds ii' ds' π 3 F = d 1 0 3 ii' ds' cos θ = cosθ d = iids' d cos θ sinθdθ π 0

F ll = = ii' ds' d π 0 3 sin 1 θ cosθdθ 3 ii' ds' sin θ sinθ d π = 0 0 ii' ds' π 1 Fll = ds r sinθ cosθ + sinθcosθ cosθ 0 ii' ds' 03 = d d cos θsinθ θ π 3 ii' ds' cos θ π ii' ds' = = d 0 d π π = θ ' =

8 1

U i = B ds (7.4.1) s dl' r B = i' (7.4.) L' 3 r r 1 = Stokes 3 r r dl' r Ui = ii' ds s L' 3 r = ii' S L ' = ii' L L' dl r dl dl' r ' ds S B ds L dui εα dt εαi B ds (7.4.4) t s dl' α = i' (7.4.5) L' r εα a i dl (7.4.6) L t a dl = B ds t t (7.4.7) L S S B ds α S L α dl α

α ε = dl t = - t = - dn dt S B ds (7.4.8) N = B ds S s ee' 1 dr r d r Fee ' = 1 + (7.4.9) r C dt C dt ee' dr e e' r dt d r dt d dl' dl ε = I' dt L L ' r = - d a dl (7.4.10) dt L

1 1 3 4

ε = dn dt

, r v = 1, Kv = 4πr K p = 0 r P = 4πr K - K N 4πr 4πr KN 4πr

= X - dp dx = Y - dp (8.1.1) dy = Z - dp dz Edσ Ed = (Xdx + Ydy + Zdz) - P + C Ed = (Xdx + Ydy + Zdz) eds e = la + mb + nc

eds = adydz + bdzdx + cdxdy da db dc eds = + + dxdydz dx dy dz da dx + db dy + dc dz = 4 πρ (8.1.4) eds = 4π ρdxdydz H dl = I dβ1 dz dγ 1 dy + β1 + dy - γ 1 + dz dz dy dβ1 dz dγ 1 dy - β1 dy + γ 1 dz dz dy β 1 dγ 1 = dz dy dydz a = d β dz - d 1 γ 1 dy b = d γ dx - d 1 α1 dz c = d α dy - d 1 β1 (8.1.5) dx

da dx + db dy + dc dz = 0 da1 + db 1 dx dy + dc 1 1 dz + 4 πρ = 0 a = d β 1 dz 0 b = d γ 0 1 dx c = d α 1 dy 0 dγ 0 + dy dα0 + dz dβ0 + dx dv dx dv dy dv dz (8.1.6) + d V dy + d d V V + 4 πρ = 0 (8.1.7) 1 dx Dz s φ α δλ = Β δσ = (8.1.10) Λ W = j adl L a E = - (8.1.11) t

p = p + 1 1 0 v v

p = p + 1 4 v p - p = 1 0 ρ 1 v 4 µ π p - p = 1 1 v (8..1) 4π µ 1 p1 p1 - p v 4π µ 1 1 px = v l p1 p y = v mn 4π µ 4π µ 1 1 pyy = v m p1 pzx = v nl 4π µ 4π µ 1 1 pzz = v n p1 p xy = v lm 4π µ 4π µ 1 1 pxx = p1 p yz = 4π µα 4π µβγ 1 1 pyy = p1 pzx = 4π µβ 4π µγα 1 1 pzz = p1 p yz = 4π µγ 4π µαβ X = d dx p d dy p d + + dz p xx xy xz 1 dµα dµβ dµγ X = α ( ) 4 π dx dy π µ d + + dz + 1 dx α + β 8 + γ 1 dβ dα 1 dα dγ dp1 µβ + αγ ( 8.. ) 4 π dx dy 4π dz dx dx

d d d dx µα + dy µβ + dz µγ dxdydz = 4 mdxdydz (8..3) 1 d d d α µα + µβ + µγ 4 π dx dy dx 1 ( ) 8π µ d α + dx β + γ µβ 1 d β d α 4 π dx dy 1 dγ dβ Y (5) 4π dy dz 1 dγ dβ = p 4π dy dz 1 dα dγ = q 4π dz dx 1 dβ dα = r (8..5) 4π dx dy

1 dα dγ + µγ µγ 4π dz dx + q X - dp 1 dx 1 d X m dx v r rq dp = α + + π µ µβ µ 1 8 dx 1 d Y m dy v p r dp1 = β + µ µγ + µα (8..6) 8π dy 1 d Z m dz v q p dp 1 = γ µ µα + µβ 8π dz dγ dβ dα dγ dβ dα = 0 = 0 = 0 dy dz dz dx dx dy αdx + βdy + γdz = dϕ αdx + βdy + γdz ϕ dϕ ϕ dϕ α = β = d γ = (8..7) dx dy dz 1 d d d m = µα + µβ + µγ 4π dx dy dz d d + + π µ ϕ ϕ ϕ = 1 d (8..8) 4 dx dy dz d ϕ ϕ ϕ + d + d = 0 (8..9) dx dy dz

ϕ = m 1 µ r dϕ = m 1 (8..10) dr µ r E = C ( α + β + γ ) (8..11) ϕ ϕ ϕ α = d β = d = d dx dy dz ϕ ϕ ϕ µ d ϕ1 d ϕ1 d ϕ + + 4π dx dy dz = m 1 1 µ d ϕ d ϕ d ϕ + + = m 4π dx dy dz ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ ϕ

ϕ ϕ ϕ 1 ϕ + d δ ϕ dx x, m., 1 1 dϕ1 E = -4 C dv x dx m dϕ 1 m dx dϕ1 dx m dv W = δ x 4 + ϕ1 ϕ1 πc = 0 δ δ ddx m dv x d dx m dv x 1 C = (8..13) 8π 1 8π ( α + β + γ ) (8..14) µ H 8π - 1 P - 1 Q - 1 R 1 π 1 1 4π P Q 4π - 1 4π R (8..15) de = - 1 (Pu + Qv + Rw)dS (8..16) dt 4 π dp P + dx x + dp dy y + dp dz z 0

dp dp puds = β γ V dz dy de 1 = ( Pu + Qv + Rw) ds dt 4π 1 dq dr dr dp dp dq = V dz dy + dx dz + 4π α β γ dy dx E = 1 ( + + )V 8π µ α β γ de 1 π µ α α β β γ V d d d = + + γ dt 4 dt dt dt α dq dr d µ α dr dp d β µ β dp dq d γ µ γ dz dy dt + dx dz + = 0 dt dy dx dt dq dr d = µ α dz dy dt dr dp d = µ β (8..17) dx dz dt dp dq d = µ γ dy dx dt dα dt H CurlE = - (8..18) t α Curla = µ H, E = - t

dh dr α dt dt i α t

m, v = m ρ, µ = πρ. m. πm

j'= j + D t D j, j' t α = Edt D A CurlH = 4 (j + ) t 4π D CurlH = j + c t

CurlH = 4 π c j divj = - d ρ dt dρ dd 4 = div dt dt 1 dd div(j + 4π dt ) = 0 1 dd j 4π dt π D CurlH = 4 c j + 1 c t α E = µ v H - - gradϕ t ϕ B B CurlE = - t 1 B CurlE = - c t

e e r r, e t + divj = 0 1 D 4π CirlH = + c t c j 0 1 B curle = c t D t.

sini1 v = sini v 1

v 1 µε 1 ε µ 0 0

hv mv w = + 1 0

e( λ, T) a( λ, T) = φ( λ, T)

a c φ(, Tλ) = c λ exp 1 λt ρ( λ, T) = Aλ 5 f ( λ, T)

v ρ( v, T) = Bv 3 ϕ t 5 c ρ( λ, T) = c λ exp 1 λt 3 bv ρ( v T ) = av exp ( 10.1) T πv ρ( v, T) = 8 kt c 3 8πv kt 3 c

πv ρ( v, T) = 8 ( 10.) 3 c

ds = du T 1 T ds 1 U = ln du av a ' v d S = (10.3) du U ds R du U U S = ln ( 10.4) av ea' v

ds du = U d S = ( 10 5) du U d S a = ( 10. 6) du U( β + U) ds du ds α U 1 = ln = du β β + U T β U = ( β/ at e 1 10.7) v U = vϕ T c1v U = (10.8) e c ' v / T ρ( v, T) = 1 3 c' v ( ' / 1 10.9) e c v T 5 c1λ ρ( λ, T) = ( ) / λ e c T 1 10.10

( W N + = P 1)! ( N 1)! P! N U = p ε N U U U U S = k + + 1 ln 1 ln ε ε ε ε 1 ds k U U = = 1+ T du ln ln ε ε ε ε U = 8/kT e -1 πv ε ρ( v, T) = 8 (10.13) 3 8/kT c e -1

πhv ρ( v, T) = 8 3 1 (10.15) 3 hv/kt c e -1 πch ρ( λ, T) = 8 1 (10.16)[4] 5 ch/ λkt λ e -1

sinδ = v sin θ ( 11.1.) c

1 1 n 1 1 v (11.1.3) n c c' = + Kv (11.1.4) n 1 K = 1 n n 1 K = 0 (3) K = 1 n 1 1 = Lc c / n Kv c / n + Kv (11.1.5)

δ = 4 n Lv K (11.1.6) cλ 1 K = 1, = 0.0. n - v / n sin δ ' = v cn sinδ = v γ c t 1 = l c + v + l c / n + Kv - v (11.1.7) t = L c - v + L c / n - Kv + v (11.1.8)

1 v K = 1 ( 11.1.7) ( 11.1.8) n c l nl t1 = t = + t = 0 c c ϕ ϕi i Ui = υ / ni s i w i si si v si v cosϕ c c n c c s i = i cosϕ s i i si v = c c i si w i i i i i i cos ϕ ( 11.1.10)

L L L t = + = ( 11.1.11) 1 c + v c v c( 1 v / c ) l ct vt = L t = c 1 v / c ( 11.1.1) 4L 1 1 t = ( t1 t ) = c 1 v / c 1 v / c Lv (11.113). 3 c c t Lv δ = = ( 11.1.14) λ λc 1 1 0 40 v 1 c 1 -

. L.,,,. v c L v c v c 3 1 t = 0,

E - 1 B (11..1) c t 1 E + 4 π B ρ W (11..) c t c E = 4πρ ( 11..3) B = 0 ( 11..4) W f = ρe + ρ B (11..5) c 1 4π E = 4π ρ + ( W c t c t ρ ) ( 11..6) 1 4π B = ( ρw) ( 11..7) c t c 1 α = 1 α ( 11..8) c t Sr = S v r t + ( 11..10) t 1 r v K = j ( 11..11) c t r xr K j x r y r zr t r = t = r

γ = ( 1/ 1 v / c ) S Q' 1 ' K' = j' ( 1113.. ) ( c v ) t r c 1 v / c S S r = v r t s ( 11.. 15 v r r c 4π E = 4π rρ c v r ( ρ v ) ( 11..16) v 4π r r B = r ( ρv) ( 11..17) c c

v r r φ = 4πρ ( 11..18) c v v E = rφ + c c r φ ( 11..19) B = v E ( 11..0) c v 1 4 + + φ = πρ ( 11..1) c x r yr zr x = x' ' 1 v / c, y = y'', z = z'', t = t'' ( 11..) r r r r '' φ'' = 4πρ'' ( 11..3) ρ' ' = ρ 1 v / c ( 11..4) φ' ' = φ 1 v / c ( 11..5) E'' = φ ( 11..6) F = F '', F = F '' 1 v / c, xr x yr y F = F '' 1 v / c ( 11..7) r t = v t c x L ( 11..8)

1 r c t L K'' = j'' ( 11..9) Br r E = - 1 r, r E r = 0 c t 1 Er r Br = r B r = 0 ( 11..30) c t v Sr S c v c v c

x' = γlx, y' = Ly, z' = Lz ( 11..33) r r r L v t' = t γ L γ c xr γ = 1/ 1 v / c, v. v, L = 1. t' x x' = γl( x vt), y' = Ly, z' = Lz v t' L t c x = γ ( 11..34) ' 1 D L Dx D ' γ L D v c H x =, y = y z ' D H H z γ L D v = + c H y 1 L H H ' γ L H v =, = + c D ' x x y y γ L H v = c D ' z z y ( 11..35)

' ' L L Fx L Fx Fy F y F ' =, =, x = F z ( 11..36) γ γ L L F(S') = L,, F(S) (11..37) γ γ 1 v / c

v = 1/ c c = 1 0 εµ ε µ ε µ 0

AB = c t' t A A

H E v c W = m c ( 1/ 1 v / c 1) 0 1 L L c v L [9] E m c

e v = E = hv 3 4 π ma h a =, 4π e m

sin θ

m( π v r) = X e r 4

1 1 vnm = R n m

h M = τ τ = 1 3 π

v = 1 ω W = τh ω ω = 1 3 π me E W = τ h 4π me E ω = 3 3 τ h τ h a = π mee -10 e 11-7 -8 e = 4.7 10 = 5.31 10 h = 6.5 10 = 1.1 10 cm, m 15-1 W ω = 6. 10 S, = 13V. e π me Wτ = 4 h τ W 4 π me 1 1 Wτ = h τ τ τ 1 1

τ τ 4 π me 1 1 v = 3 h τ τ 1 10 e 11 7 ε = 4.7 10 = 5.31 10 η = 6.5 10 m π me 4 3 = 3.1 10 15 h 1 ~v = R H n =.5,3,3.5,4, 1 n 1 1 ~v = 4RH n n 1 1 ~v = 4RH n = 5,6,7, 4 n 1

~v R n H = 1 1 mm m M +, M

ö

W = hv = m c 0 1 v / c w n dn k T e kt W dw W = 3 3 ( E E) = nhve n πhv n= 1 kt E n = 8 hv 3 π υ e n = 1 3 3 c E V E = n= 1

W = m 0c = hv 1 β p = m 0υ h υ = β = 1 β λ c µ W = 0 c = hv 1 β 0 µ υ p = = h [4] 1 β λ Ldt = 0 Tdt = 0 1 δ [ ( )] / m E U ds = 0 δ n c ds = 0 1 [m(e - U)] u = c / n

1 c u = [ m( E U)] n t t 0 Ldt configura - tion space S actionsurface p = S = -E(E t ϕ = πv ϕ = -ωt + k r k = ϕ = -ω t h., π

m0c v 0 v = = h 1 β 1 β v = v 1 β, sinπv 1 0 1 x sinπv 1 υ x 1 β sinπv t = sinπvx c / β v c 1 β sinπv x = sinπvx υ υ c

nds = 0 ds δ = vds δ λ υ δ m βc c = 0 h υ c ds = 0 / 1 / mυds = 0 δ m0( βc) m0βc dt = δ ds = 0 1 β 1 β v v = v + dv = + d υ υ υ dv dv

vx v' x sinπ vt + ϕ sin π v' t ϕ' υ + υ' + cos π δ d v v υ dv vx = t x + ϕ' sinπ vt + ϕ dv υ 1 υ g d v υ = dv c 1 m 0c υ = v = β h 1 β d v dv υ υg = dβ dβ dv m0c β = 3/ dβ h ( 1 β ) d v β d υ m c 1 β 0 m0c 1 = = dβ h dβ h ( 1 β ) c / υ h λ = = m c / h m υ 0 0 λ = h m υ. 3/

t c = υ( t + T) υ β t = T 1 β m0c Tβ πv1t = π h 1 β m0c Tβ π = πn (n ) h 1-β m0β c T = nh 1 β ( p dx + p dy + p dz) = nh T x y z ( p dx + p dy + p dz) 0 T 0 x y z T m 0 m0β c = ( υ x + υy + υ z) dt = T 0 1 β 1 β = nh mωr n h = π v υ v dl = n υ

1 m0c υ = c / β, u = βc h 1 β nv dv = 4 π 4π v dv = β v dv 3 uυ c m0c hv = = W m0c = m0c ( 1+ a) 1 β 4π n dv h m c a a a dw v = 1 + + 3 0 ( ) ( ) 1 1 ne e nhv kt nhv kt 4π dnw = c m c( 1 + a) a( a + ) dwdxdydz h 3 0 1 1 ne e nhv kt nhv kt w 4π 3/ dnw = c m W kt Wdxdydz h 3 0

V 1 3

ö

ö

( I) H( q, S ) = E. q ( I') H q, K ψ = E ψ q S H q = E (14..1) q S q p S q q

k ϕ H q = E (14..1 ) ϕ q T = 1 ( px + pv + p z ) m 1 k ϕ = + m x ϕ + y ϕ ϕ z V = - e (r = x + y + z ) r H = T + V = 1 k m ϕ = E ϕ ϕ ϕ + x + y z ϕ ϕ ϕ + x + y z - m e E + ϕ = 0 ( 14..1 ) k r ϕ ϕ ϕ m e δj = δ dxdydz + ϕ x + y E + z k r = 0 ( 14.. 3) 1 δ δϕ ϕ m e J = df dxdydzδϕ ϕ ϕ 0 + n E + = k r ( 14.. 4) m e ϕ + E + ϕ = 0 ( 14.. 5) k r dfδϕ ϕ = 0 ( 14.. 6) n e r

m m = x(r)u( θ ϕ) u P (cos θ)cosm ϕ (cos θ)sinmϕ l d x me n n 1 + dx dr r dr + me ( + ) + x = 0 (14..7) k k r r 1 E E r me = n k me me E = 4 n = 1, (14..8) k n k k = h π E = - 4 π me (14..8'') h n E v = E h - E 1 h l

W t (14.3.1) W W = (Ttc W T q k = E - V (14.3.1 ) q k (ds) = T(qk,qk)(dt) (14.3.3) W (14.3.1') gradw q k gradw = (E - V) (14.3.1''') dw0 ds = (14.3.4) (E - V) t

Edt ds = (14.3.5) (E - V) u = ds dt = E (14.3.6) (E - V) p ds p ds E V t T O u E E dt ti = δ = δ ( ) = = Tdt p δ 1 p t E δ 1 1 t 1 1 ( 14.3.7) W p k = (14.3.8) q k 1 E 14.3.3 u υ ds = T = (E - V) (14.3.9) dt

πw πετ πs( q k) sin + = σιν + + (14.3.10) h η h v = E (14.3.11) h λ = u v = η (14.3.1) (Ε ς) υ = dv d( v (14.3.13) u )

- 1 "= 0 (14.5.1) u 8π ϕ + (hv - V) ϕ (14.5.1') h 8π ϕ + (Ε ς) ϕ = 0 (14.5.1 ) h η ϕ + ςϕ = E ϕ (14.5.1''' ) 8 π µ

ϕ πie = = t h ϕ E = h πi t η + ςϕ = η ϕ ϕ (14.5.) 8π m πι t

ö