(5) t = 0 θ = 0 a θ = 2 ag (a) θ λ (b) cos θ 3

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

(5) t = 0 θ = 0 a θ = 2 ag (a) θ λ (b) cos θ 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

I-3 ( ) (100 ) H = 1 2m p2 + 1 2 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 + 1 2 ) (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

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

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

(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

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

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

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

(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

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

(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

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

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 + 1 + 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

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

III-4 ( ) (100 ) T x u x t u t = u a 2 x 2 a a = 2.53 10 7 m 2 /s (A) (1) (A) x u(x, t) = A 0 + 2 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 ( ) 2 1 + 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 = 60 60 24 365 3.15 10 7 s 15 C 15 C ( ) 2π f(t) = 15 + 15 cos T t (F) x exp( π) = 0.043 8

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III-7 ( ) (100 ) (1) (a) (b) 8.00 10 7 m 1.00W 1 c=3.00 10 8 m/s h=6.63 10 34 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

(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

n a C X III-8 ( ) (100 )! #"%$#&')(+*,-/.0132%45.60782:9+; <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$8-5e6 F.0 9 e1fjk 45 ;PO (2) (σ ) =.60)Fj%4 9 q1-19 6.60 # #.606JKt{ 7 m ˆ (a) v δr (Lagrange ª6«++C * P}D~ H- ) (C) s 9?45 ž = ( ~h -i 6 v #.06j { m u # ˆD4 B(r + δr) v(r, t) 6}- = ) d δr = (δr ) v. dt (C) : A(r),.01' dd4 96a5I+3 7±AB6C ' ²³z 9ŒC 4 (b) ρ ( ) (B) E7G8I *7 4h vµv; =1 3m s? σ B/ρ Lagrange 9 C 9?4 ¹6ºba^I s19$r PS568.0l99p»#{hJKq!- ª«s (C) 9?4h 7ž =%s v4?66¼6 6½:9h¾ Alfvén <= {F±Ã ( 7ÀÁ 16 )

(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 = 3.0 10 6 [rad/s] 6 FG r = 7.0 10 5 [m] H /jdš 9^]_P 8D Et4 V = 4.0 10 2 [m/s] r 0 = 1.5 93a^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

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