(5) t = 0 θ = 0 a θ = 2 ag (a) θ λ (b) cos θ 3
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- あきひろ かんざとばる
- 7 years ago
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1 I-1 ( ) (100 ) a m g (x, y) y x y y x θ (1) (r, θ) x = r sin θ, y = r cos θ (r, θ) r = a λ(a r) λ (2) (a) (r, θ) λ (b) λ (3) θ 3 θ θ t = 0 θ = θ 0, θ = 0 θ = dθ dt (4) (3) t = 0 θ = π/2 θ = 0 T F π/2 0 dθ(cos θ) 1/2 T ( ) 2
2 (5) t = 0 θ = 0 a θ = 2 ag (a) θ λ (b) cos θ 3
3 I-2 ( ) (100 ) µ 0 R M M B = µ 0 (H + M) z (1) H in B in H out B out n t (2) H φ φ Laplace (3) H B z Laplace a n, b n φ = n=0 ( a n r n + b ) n P r n+1 n (cos θ) P n (x) = 1 d n 2 n n! dx n (x2 1) n Legendre (1) H B (4) µ 0 2 H M dv = µ 0 2 H 2 dv 4
4 I-3 ( ) (100 ) H = 1 2m p mω2 x 2 (A) x p ω m H ψ n = E n ψ n (B) ψ n E n n (n = 0, 1, 2, ) (1) a a mω a = 2 h (x + i 1 mω p) a = mω 2 h (x i 1 mω p) [x, p] = i h a,a [a, a ] = 1 H = hω(a a ) (2) N a a N ψ 0 a ψ 0 = 0 ψ 0 ψ 0 ψ 0 = 1 n ψ n (C) (D) (E) ψ n = 1 n! (a ) n ψ 0 (F) E n ψ n ψ n ψ n = 1 (3) ψ x ψ l ψ p ψ l ( ) 6
5 x p x ϵ (1 i 1 h ϵp) ψ 0 (G) t = 0 (G) ψ(t) (4) t = 0 ψ(t = 0) ψ n ψ(t = 0) = n C n ψ n (H) C n (5) ψ(t) x x = ψ(t) x ψ(t) p p = ψ(t) p ψ(t) En i ψ n ψ n (t) = e h t ψ n X x, Y p (X, Y ) X-Y t = 0 7
6 II-1 ( ) (100 ) (1) α, β V α, V β N α N β N = N α +N β α, β (a) α V α V α +V β Boltzmann T (b) V α + V β α, β V α + V β α, β C D, A B V α + V β C D β A B α 1 ( ) 2
7 (c) α φ(= Nα N ) S = N[φ log φ + (1 φ) log (1 φ)] (A) (2) N α β N α N β N 1 N α α N β β 1 (a) N α, β (b) (A) Stirling log x! x(log x 1) (B) (3) α β α α ɛ αα β β ɛ ββ α β ɛ αβ z U = Nχφ(1 φ)t (C) χ (4) F φ, χ, T χ F φ χ 3
8 II-2 ( ) (100 ) (1 + v)=2 (1 v)=2 (1) t t p P t =0 p =1 (2) (a) jvj fi1 t fl 1 n! ß p n n 2ßn e x 2 t x; t; v p t+x 2 ß s 2t ß(t 2 x 2 ) ff t 2 fi ff fi p (b) jvj jxj=t O(1= t) fi 1 (1+v) x 2 ß e vx 2 t x x + dx f (x; t)dx x(= 2 t) 2 f (x; t) ß p2ßt 1 exp (fl); x 2 ; fl (3) t =0 x =0 (> 0) [t; t + dt] p (t)dt x θ 0 0 t t t x> f (x; t) = Z t 0 dt 0 f (x ; t t 0 )p (t 0 ) (A) 4
9 R 1 0 dte st p (t) ψ Z 1 1 dt 0 pßt exp z2 4t st Z ψ 1 jzj dt 0 2 pßt exp 3! z2 4t st = 1 p s e jzjps ; (B)! = e jzjp s (C) 5
10 II-3 ( ) (100 ) 1 η m x Aη dx dt m d2 x dt 2 dx = x Aη dt (A) x = Ce gt g 2 + 2αg + ω 2 0 = 0 (B) α = Aη 2m ω 0 = m (1) t = 0 x = 0, dx dt = v 0 α > ω 0 α < ω 0 x(t) x(t) (2) α < ω 0 α ω 0 α = ω 0 x(t) 1 ( η x 1,x 2 (3) 1,2 ( ) 6
11 (4) x 1,x 2 q 1,q 2 q 1,q 2 ω 1,ω 2 d 2 q 1 dt 2 + 2αdq 1 dt + ω2 1q 1 = 0 d 2 q 2 dt 2 + 2αdq 2 dt + ω2 2q 2 = 0 (C) (D) (5) t = 0 x 1 = x 2 = 0, dx 1 = v dt 0, dx 2 = 0 η = 0 dt 1,2 η η c η c x 1 (t), x 2 (t) e γt [B 1 sin (Ω 1 t + b 1 ) + B 2 sin (Ω 2 t + b 2 )] (E) t Ω 1 Ω 2 Ω 1,Ω 2,B 1,B 2 ) 7
12 III-1 ( ) (100 ) (1) φ(x, t) A(x, t) E(x, t) B(x, t) E(x, t) = φ(x, t) A(x, t), B(x, t) = A(x, t) (A) t (a) Maxwell ρ(x, t) j(x, t) D(x, t) = ρ(x, t), H(x, t) D(x, t) t = j(x, t) (B) D(x, t) = ε 0 E(x, t), H(x, t) = c 2 ε 0 B(x, t) c ε 0 A B(x, t), E(x, t), B(x,t) t Maxwell (b) A A(x, t) + 1 c 2 φ(x, t) t B = 0 (C) A B φ A K (L M) = L(K M) (K L)M (D) (2) e m x e (t) ρ = eδ 3 (x x e (t)), j = eẋ e (t)δ 3 (x x e (t)) ȧ(t) = da dt (a) m d2 x e dt 2 = ee(x e, t) + eẋ e B(x e, t) (E) Maxwell [ d 1 dt 2 mẋ2 e + 1 ] d 3 x (E D + B H) 2 = d 3 x (E H) (F) (L M) = M ( L) L ( M) (G) ( ) 2
13 (b) c E(x, t) = e [x (x v)], 4πε 0 c 2 r3 x E B(x, t) = rc (H) r = x v = ẋ e (F) S = e 2 v 2 /(6πε 0 c 3 ) a ω S 3
14 III-2 ( ) (100 ) H = H 0 + λv λv H 0 H 0 ε (0) φ ( = 1, 2,...) (0) ε (0) λ 0 λ 1 (1) φ (0) H ε φ φ λ 0 λv φ (0) ε = ε (0) + λε (1) + λ 2 ε (2) +... (A) φ = φ (0) + λ φ (1) + λ 2 φ (2) +... φ φ H φ = ε φ (0) φ = φ (0) = 1 φ (0), ε (1) φ (1) ε (2) ε (0) φ (0) (B) V (2) ε (0) H 0 ε (0) φ (0) α α φ (0) α φ (0) H 0 α = ε (0) φ (0) α φ (0) α = δ αα φ (0) α H 0 ε (0) φ (0) = α φ (0) a α α (C) a α (D) 4
15 ε (1) (3) n = 2 1 2s (l = 0 m = 0) 3 2p (l = 1 m = 1, 0, 1) Bohr a ψ nlm (r, θ, ϕ) = a 3/2 g nl (r/a)y m l (θ, ϕ) (E) Yl m (θ, ϕ) ( ) 1 g 2s (ρ) = (1 ρ/2) e ρ/2 (F) 2 ( ) 6 g 2p (ρ) = ρ e ρ/2 (G) 12 z E = Eẑ e eer cos θ eer cos θ 1 ε (1) n Linear Star Effect 2π 0 dϕ π 0 cos θ Y m l = sin θdθ Yl m (θ, ϕ)yl m (θ, ϕ) = δ mm δ ll (H) [ (l m)(l + 1 m) (2l + 1)(2l + 3) ] 1/2 Y m l+1 + [ (l + m)(l m) (2l + 1)(2l 1) ] 1/2 Y m l 1 (I) 5
16 III-3 ( ) (100 ) (1) H s = ±1 sμ B H μ B T B hsi S, H H 0 H < 0 (2) N (fl 1) J=N P s H eff m = j s j =N H eff = J μ B N X j(6=) s j = J μ B (m s N ) ß Jm μ B T Jm=μ B hs i m, self-consistent equation m 6= 0 T c (3) E = J 2N XX i6=j s i s j = J 2N ( NX i=1 (A) s i ) 2 + J 2 ß NJ 2 m2 (B) m ß 0 m = ±1 NJ=2 e NJ=2BT e S B ln 2 ß 0:69 6
17 III-4 ( ) (100 ) T x u x t u t = u a 2 x 2 a a = m 2 /s (A) (1) (A) x u(x, t) = A A n e αnx cos (nωt α n x + φ n ) n=1 (B) ω = 2π nω T, α n = 2a (C) φ n t x i = ( ) 2 ( ) i 1 i, i = 2 2 (D) (2) f(t) = a 0 + (a n cos nωt + b n sin nωt) (E) n=1 (B) (3) 1 T = s 15 C 15 C ( ) 2π f(t) = cos T t (F) x exp( π) =
18 "! N%#8$<&( PO<Q D R8ST6U *+/GVXW 3<5Y6DZ[9'\]7^9+N43'5_Y<*3[54`"a[b cd_ebf 9g\Ghji/ V U W3[5_Y[D+Z69g\jlGV U W monj7g9'\]7g9+ngp*lgv<*4q[b;i"rxs?tlu%v w%x D_y<H i f 9 zo'q D2{ U *-l8vgwgn) -94}Ja~b Tˆ {!ƒ ŠŒ! {< eg MŽ( g9;n!"f 9 O?Q Dn 9+lGV"q^WLi ŠŒ! *_}%a w"x Dy 8\- i^š"* R"S b T e i8 oœ" Bž[b T Ÿ eof 9?p?\ 14 X "NG h]i exf 9N c {!ƒ ª OgQ *+«w 1ˆ G 6\L ˆiJ#8$g&(*+=o>gb RJS e T ª \ ) ±i0²j³%i<š%*+@ja bgrxsgtgu"v w"x * Bœ" Jž \µk'm8i[ ;HB* e T ª! Ÿ \4ō9+N;y2 C[b T ª T ª! Ÿ T ª! Ÿ \4 ¹ š2 4ºGWGi%@JAJ»6b'p+?ºB¼ e bj %H N8½X¾o& (À < IÂÁˆ9_/8V)ÃÀ@%A%»\4ō9 p4 '1ˆÄ"Å0/\ˆHŽ! N+½o¾0& (ˆb;i ÆO^Q D R SÇJU */8V?W 3[5_Y6D+ZÈ i6p;*_qã_rxs?tgu%v w"x Dy ŒNÉ[D+i ª O^Q «w h +ÊED_3E5+YEDJ XËB l8vž1ˆì6í05g7":[dgãî@jaž1;n L9;NŽp+ i^r?s[t"ujv w%x D+y<Hoš%*_ oœ" Bž[bŽÏ exf 9;NG=o>G@JA0C21+Ð^Ñ 9"DJbi)p4 (BÒÓFX*;@%AŽ1ˆÔgILÕ'Öoº ÙØ?Ú_Û'*+@JAŽ1Ü8Ýg7'94ÞBß^W f 9;N íoî à! ²Gá<D+i_â"ã<ḠrosXtLu%v wgx^e0f 9 {! \ ä {! D%š?å -y Ó}"a æ qe*+ç 1_K'M^96\Ài[šB* wjx *_ oœb Bž6b TÂègÇ! Ÿ \_?9NŽp 61K é ĥ ILi ª O^Q *_«w 1?ĥ I Ì'Ío5<h+ ˆN h]i T i Ç ijï'b ê Q D^?( ë"²8ì exf 9;N! D;i%ï(? ;=X>G@JAJC6DGF0H"ILKJð^7g9;N Ò! w! w ê Q ÏXW-ñ6*;@JA~D+C^ò0I8ó D ô2 6Áõñ6*;@JAgW-öB.X,8 < ;øjù p4 [1ˆÌ<Í 56h]@BAûú übte +\þýÿ i"=^>8@0a0c21 à 6ÁÀ7[9%DBb i"«1 D<h; B¼L % 2( e ½X¾^*^9+W%»\4 X ;IJHX9?Ã* W)à ĥ I i?š"* ñ6*+@%a'w-öj.o,8 < +øbù p [14Ä"Åo/úLü%tE +\µýè! i8=o>g@jabce1 à [ÁÀ7g9"D%bi"«w ê Q 1 D<h+ 0¼- J 2(4 %H"& Ø%DûÁ!
19 :<*!%ì e b i"365+y6*!"jù$#0i%&[d('h Q ) M +*L! «w h,~¼o9-6b e L "H Ngšgp e i /. *+«w ê Q 1 ) M 10 ª \%h4ili p *+«w 1 +*Je324. Á 65h]i7oïÂh 8XØ^ÚB19h]ù :B [9[\H) <;>= 14 ÿ õn p-*;øbùoi þø?ú+û *+«w ê Q3? b 2 0 ª \_ō9;n w ê Q \ f í D w ê Q e %&~D A'H8#"$[&Â(+* /21_ _øoù?i0²"á2DBb B. * «WDC6H Ì'ÍB5<hÀ@%Aÿú-üJt6 D8 ) ±i 9E$F #$'ÿá]ō9<\µä"å0/úlü%t6?9 N µø^ú+û'*«w G~ H? ²Gì!ƒe^f ê'di"ì6ío56h]@ba ú-ü%t6 Ù*8oØXÚ"1I >F)ÃJ7Jï¹ĥ I49Âhþù :% '9ˆø%ù\þiLÄ"Å0/ú-ü%t~ Ó* 8oØXÚ"1I $F)ÃJ7Jï¹ĥ I49Âhþù:% '9ˆø%ù b;ilk!m<( W \Gĥ b;ï21 7g9-& c
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22 III-7 ( ) (100 ) (1) (a) (b) m 1.00W 1 c= m/s h= J s (c) λ v λ (d) λ M E v (e) 1 J=0,±1 1 S 0 3 P n n=0,1,2 3 P 2 3 P 1 3 P 0 1 S 0 1: ( ) 14
23 (f) λ/4 λ/4 (2) 2 2 (a) S1,S2 A 1,A 2 r exp(ir) x S1,S2 l x, l d =2π/λ λ r (b) 3.16cm l=10.0cm d=2.00µm (a) (c) S2 S2 S1 4% S1 x d/2 d/2 x=0 S2 l 2: 15
24 n a C X III-8 ( ) (100 )! #"%$#&')(+*,-/.0132% :9+; <3= 621?>@6ABCD4FEHG8I.01FJKD4/LNM8;PO =QR *S#7T7U V1WNXZY+[6\6C%4^]7_8`Eba5I);?G = (A B) = A( B) B( A) + (B )A (A )B, ( A) = ( A) A. cd?egf4h66 i.60j *JKlahIG- =Hm (1) 4hoj:93ahIp B 9rqP- σ =ts3u+.0vi. v +6e c v c j E wix?y6z S?C H;PO5{i P}%~ v- (Ohm ) (A) = j = σ (E + v B). 45 s6s * }8IG-/6e.60v? 6ƒ)(? 1 #Hu? ˆvF l, τ $Š79 q!-p9œ ie F 6Ž36.t4 qh- s 9 *P$+- = l/τ v c m +6.60PSiP(6{ h *7,-P9 qv- =)sfe6 ABCvSpT Maxwell UH;POh{i ) - = E = 0, B = 0, E = B t, H = j. s6s *p6ed4 vf 8 D4 9rqP-v9Œ *,- H µ 0 B = µ 0 H = 3šp 68 SF 8œ 9rqH- =)sie6 38c6dP3u i 6ˆ7pC * H} σ (B) ~ P- s 9#4h 7ž = B t (A) 1 = (v B) + B. (B) µ 0 σ Ÿ 6 *1$8-5e6 F.0 9 e1fjk 45 ;PO (2) (σ ) =.60)Fj%4 9 q # #.606JKt{ 7 m ˆ (a) v δr (Lagrange ª6«++C * P}D~ H- ) (C) s 9?45 ž = ( ~h -i 6 v #.06j { m u # ˆD4 B(r + δr) v(r, t) 6}- = ) d δr = (δr ) v. dt (C) : A(r),.01' dd4 96a5I+3 7±AB6C ' ²³z 9ŒC 4 (b) ρ ( ) (B) E7G8I *7 4h vµv; =1 3m s? σ B/ρ Lagrange 9 C 9?4 ¹6ºba^I s19$r PS568.0l99p»#{hJKq!- ª«s (C) 9?4h 7ž =%s v4?66¼6 6½:9h¾ Alfvén <= {F±Ã ( 7ÀÁ 16 )
25 (3) ¼ 8½v t9,t~ 6{i Pi 8e H,- = {8S ~1{6-h P(8?8e!,- = +m ~hs N9p;H-h686P /HG?"!#$ %8&'v i v ()v{i."ha IG7- =1s "!#$%*+1,.- SF 0/218JKP m µ{ ÁP 3,54#iY v{3 - = ¼ 8½ ~ 6 0!#$%{;879 ~;:7$6Š/ m + g» s <!#$% 3,54#iY,=- 4p <> m ÁP %4@?A s 9i{8 - (B 1) =Ds6s *7S?< C ~5DE S C r 10r (r F<G ) *7S?H6 I*)J m e C )"!K#$%S?K G A8L6{ *p\8j"m? V JKt4FqH-7»? )9 qp- = N Ogf{8,-P PF8e t{ w a^ipt UQ{ R }v; = Kẗ989p»?{Rp HS+j6 *TU1q!-@I*J m V!#$ %hj6k (a) ω 4# }# si7*7 5!4 ;WN9rqH- {8,- 3,A4 #FY88e)?3 (\ 4@!q+ABCD4h 1µP; ) = 2 X YZ[ (r, φ) *+ r 10r 0/21S3j (b) ω = [rad/s] 6 FG r = [m] H /jdš 9^]_P 8D Et4 V = [m/s] r 0 = a^Ip)]_* O<` a!*p+ N9Œ D92]_ 4h < P8 q 10 8 [m] S ψ 4h vµp; = B N O<DfF* P 3,54#FY38e = 1: S C 6P?3 4;q = V S 0!#$% /j B 17
26 1 III-9 ( ) (100 )! 7H'I0J?KML%GNPOPQC:R+%<TSVUW578XI#NYOPQ I[Z]\_^Y`!aPb &cq \edpf"cbgt&h5y78;ij!a4l/:r+/scim(rn&o";ppug$&[(wqr.w7p8 +0<GwPx%"myz9{!.0798R243 s?tuw}?~pg +m<?243ym 9ƒ H "P GH " D%F 7PH U? ]ˆ_v+I "4! ]ˆ[UWŠ8 ( (H 0 ) (H + =p) (e ) r[m] CŒ + A!Ž4A UG T " " I6:+W</. n H 0(r) [m 3 ] n p (r) [m 3 ] n e (r) [m 3 ] "V78293 st De ]ˆ + 59H U0 9 P"4 / %šh UW œ (Cn4+ U7 H 8 Ÿž9 W ;:+W< W / V P d9f(9* +I6:+m< 0 H 0 $9 (1)? * B &)U05Y9"9b!gp&ª5P9 9 «!b (1 Hz) L ν (ν) [J s 1 Hz 1 ] P9! ]ˆ Š8 U ( Z V" 9 r[m] / 4 (1 m 3 )?! * B (1 s) &h 9 /U +G 4< B9±e"%79895H(mz :!+ U² ³P Vµ H 0 H I:+%< g B " S U (% ¹ [gvºc(w78p5phrav7p8p(w»c¼ 0 A a(ν) [m 2 ] ½E+[¾Y ȩ? ;º Á+I:R+W< =Y>Y" ; 1C* B &( ÁP+WNCOYQpUG TV"9NCO Q ÂP à (2) I? " P ºWÄ/ Eˆ A +0<?Å[Æ;ºY*+[ ƒ!u[çq β [m 3 s 1 ] mè;z 4"5P78Yi9jUmÉT[Ê n p (r) n e (r) β ξ(r) = n H 0(r)/n Œ < B± " º;* +W< H (r) n H (r) = n H 0(r) + n p (r) wcxv"7p8e293vstìë0cº=íu "9 P/ ˆ 1 ( n H = [m 3 ] +7 8P5YHpU 9 a ºC*;+0Ï;QMV;!+G</. / " [s 1 ] a(ν) 7Y8P5 HEUG$Y (%Ð'ˆÑ=9Í!º I#Ò;ÓÔm?ÕZ?<g B " ν º * +W< a [m 2 ] β [m 3 s 1 ] º%Ö/ B ÉC Mˆ_" ( Œ + ؾ Ù =?Ú ºVÛ?ÜYÝEn< (3) (2) r = [m] ξ S9SVgGºV" H!aGÞEÅ ºG798(%»Y¼ A V½+ ¾ p[ 9 [ Á B <E (4) " P9! ˆ ß]àm!+(4b A V"ES%U0¾ T[ 9 ;ºÁG.à á. +m< S%U0¾ p[â9ã :!+ B P(m" $9 «pä B U079895H!aV" ν [Hz] N ν (ν) [Hz 1 ] åyæ UmyçR ]ˆ U0y9çCèé9À9Š98 ±PŒê/ë ± IVÁ U r [m] r + dr [m] dr [m] PìYí mècz Gî!Ý9< dn ν (ν) [Hz 1 ] ξ(r) st IW U%ï U Å0Æ2934st ImUWð ñmugs9tm ò ópst I?nGô4< (5) SGUWstT[õ9^!:/+ ö;(079859heu0 /a (m½e+ De z UW I 1/e (e ) ;+;S [ؾ9 9ÙC=Ú;ºVÛÜ;ÝEn < B9± "TS%U ste( Z I_ÒYÓÔ n%z4< ξ 0.5 (6) 79823Vst UmåPæEؾ9 9Ù;=Ú;º4ÛÜ;Ýpn <4úû.Tˆ π 1/ È;Z n%z?< 18
18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α
18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α 2 ), ϕ(t) = B 1 cos(ω 1 t + α 1 ) + B 2 cos(ω 2 t
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4. ϵ(ν, T ) = c 4 u(ν, T ) ϵ(ν, T ) T ν π4 Planck dx = 0 e x 1 15 U(T ) x 3 U(T ) = σt 4 Stefan-Boltzmann σ 2π5 k 4 15c 2 h 3 = W m 2 K 4 5.
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199 1 1 199 1 1. Vx) m e V cos x π x π Vx) = x < π, x > π V i) x = Vx) V 1 x /)) n n d f dξ ξ d f dξ + n f = H n ξ) ii) H n ξ) = 1) n expξ ) dn dξ n exp ξ )) H n ξ)h m ξ) exp ξ )dξ = π n n!δ n,m x = Vx)
1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0
1 No.1 5 C 1 I III F 1 F 2 F 1 F 2 2 Φ 2 (t) = Φ 1 (t) Φ 1 (t t). = Φ 1(t) t = ( 1.5e 0.5t 2.4e 4t 2e 10t ) τ < 0 t > τ Φ 2 (t) < 0 lim t Φ 2 (t) = 0 0 < t < τ I II 0 No.2 2 C x y x y > 0 x 0 x > b a dx
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[1.1] r 1 =10e j(ωt+π/4), r 2 =5e j(ωt+π/3), r 3 =3e j(ωt+π/6) ~r = ~r 1 + ~r 2 + ~r 3 = re j(ωt+φ) =(10e π 4 j +5e π 3 j +3e π 6 j )e jωt
![[1.1] r 1 =10e j(ωt+π/4), r 2 =5e j(ωt+π/3), r 3 =3e j(ωt+π/6) ~r = ~r 1 + ~r 2 + ~r 3 = re j(ωt+φ) =(10e π 4 j +5e π 3 j +3e π 6 j )e jωt](/thumbs/101/152334931.jpg "[1.1] r 1 =10e j(ωt+π/4), r 2 =5e j(ωt+π/3), r 3 =3e j(ωt+π/6) ~r = ~r 1 + ~r 2 + ~r 3 = re j(ωt+φ) =(10e π 4 j +5e π 3 j +3e π 6 j )e jωt")
3.4.7 [.] =e j(t+/4), =5e j(t+/3), 3 =3e j(t+/6) ~ = ~ + ~ + ~ 3 = e j(t+φ) =(e 4 j +5e 3 j +3e 6 j )e jt = e jφ e jt cos φ =cos 4 +5cos 3 +3cos 6 =.69 sin φ =sin 4 +5sin 3 +3sin 6 =.9 =.69 +.9 =7.74 [.]
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II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2
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II No.1 [n/] [1]H n x) H n x) = 1) r n! r!n r)! x)n r r= []H n x) n,, H n x) = 1) n H n x) [3] H n x) = 1) n dn x e dx n e x [4] H n+1 x) = xh n x) nh n 1 x) ) d dx x H n x) = H n+1 x) d dx H nx) = nh
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128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds = 0 (3.4) S 1, S 2 { B( r) n( r)}ds
127 3 II 3.1 3.1.1 Φ(t) ϕ em = dφ dt (3.1) B( r) Φ = { B( r) n( r)}ds (3.2) S S n( r) Φ 128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds
.2 ρ dv dt = ρk grad p + 3 η grad (divv) + η 2 v.3 divh = 0, rote + c H t = 0 dive = ρ, H = 0, E = ρ, roth c E t = c ρv E + H c t = 0 H c E t = c ρv T
NHK 204 2 0 203 2 24 ( ) 7 00 7 50 203 2 25 ( ) 7 00 7 50 203 2 26 ( ) 7 00 7 50 203 2 27 ( ) 7 00 7 50 I. ( ν R n 2 ) m 2 n m, R = e 2 8πε 0 hca B =.09737 0 7 m ( ν = ) λ a B = 4πε 0ħ 2 m e e 2 = 5.2977
9 1. (Ti:Al 2 O 3 ) (DCM) (Cr:Al 2 O 3 ) (Cr:BeAl 2 O 4 ) Ĥ0 ψ n (r) ω n Schrödinger Ĥ 0 ψ n (r) = ω n ψ n (r), (1) ω i ψ (r, t) = [Ĥ0 + Ĥint (
9 1. (Ti:Al 2 O 3 ) (DCM) (Cr:Al 2 O 3 ) (Cr:BeAl 2 O 4 ) 2. 2.1 Ĥ ψ n (r) ω n Schrödinger Ĥ ψ n (r) = ω n ψ n (r), (1) ω i ψ (r, t) = [Ĥ + Ĥint (t)] ψ (r, t), (2) Ĥ int (t) = eˆxe cos ωt ˆdE cos ωt, (3)
(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0
1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45
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[ ] 7 0.1 2 2 + y = t sin t IC ( 9) ( s090101) 0.2 y = d2 y 2, y = x 3 y + y 2 = 0 (2) y + 2y 3y = e 2x 0.3 1 ( y ) = f x C u = y x ( 15) ( s150102) [ ] y/x du x = Cexp f(u) u (2) x y = xey/x ( 16) ( s160101)
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ii p ϕ x, t = C ϕ xe i ħ E t +C ϕ xe i ħ E t ψ x,t ψ x,t p79 やは時間変化しないことに注意 振動 粒子はだいたい このあたりにいる 粒子はだいたい このあたりにいる p35 D.3 Aψ Cϕdx = aψ ψ C Aϕ dx
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微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.
微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)
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ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 +
2.6 2.6.1 ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j (2.121) Z ω ω j γ j f j
) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8)
4 4 ) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8) a b a b = 6i j 4 b c b c 9) a b = 4 a b) c = 7
50 2 I SI MKSA r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq
49 2 I II 2.1 3 e e = 1.602 10 19 A s (2.1 50 2 I SI MKSA 2.1.1 r q r q F F = 1 qq 4πε 0 r r 2 r r r r (2.2 ε 0 = 1 c 2 µ 0 c = 3 10 8 m/s q 2.1 r q' F r = 0 µ 0 = 4π 10 7 N/A 2 k = 1/(4πε 0 qq F = k r
量子力学 問題
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II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )
II 214-1 : October 2, 214 Version : 1.1 Kawahira, Tomoki TA (Kondo, Hirotaka ) http://www.math.nagoya-u.ac.jp/~kawahira/courses/14w-biseki.html pdf 1 2 1 9 1 16 1 23 1 3 11 6 11 13 11 2 11 27 12 4 12 11
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Holton 9.2.2 semigeostrophic 1 9.2.2 semigeostrophic,.., Φ(x, y, z, t) = (p p 0 )/ρ 0, Θ = θ θ 0,,., p 0 (z), θ 0 (z).,,,, Du Dt fv + Φ x Dv Φ + fu + Dt DΘ Dt + w dθ 0 dz = 0, (9.2) = 0, (9.3) = 0, (9.4)
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