t = h x z z = h z = t (x, z) (v x (x, z, t), v z (x, z, t)) ρ v x x + v z z = 0 (1) 2-2. (v x, v z ) φ(x, z, t) v x = φ x, v z

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1 I 1 m 2 l k 2 x = 0 x 1 x 1 2 x 2 g x x 2 x 1 m k m 1-1. L x 1, x 2, ẋ 1, ẋ 2 ẋ 1 x = Q = x 1 + x 2 2 q = x 2 x 1 l L Q, q, Q, q M = 2m µ = m Q q x 2 = h 1 x 1 t = t x 1 (t) x 2 (t) 1-5. x 1 x 2 p 1 p 2 Q q P p P p p 1 p Q, q, P, p H N q i, p i (i = 1 N) f(q i, p i ) H(q i, p i ) df N dt = {f, H} ( f H f ) H q i p i p i q i i=1 1-6 H(Q, q, P, p) = H Q (Q, P ) + H q (q, p) H Q H q H Q H q

2 t = h x z z = h z = t (x, z) (v x (x, z, t), v z (x, z, t)) ρ v x x + v z z = 0 (1) 2-2. (v x, v z ) φ(x, z, t) v x = φ x, v z = φ z (1) 2 φ x φ z 2 = 0 (2) v z (x, z = h, t) = 0 (3) g φ z (x, z = 0, t) + 2 φ (x, z = 0, t) = 0 (4) t2 g φ φ(x, z, t) = f(z) sin(ωt kx) k (> 0) φ(x, z, t) h (kh 1)

3 II 1 a b c a < b < c r ɛ 0 -Q +Q a c b Q Q r E(r) 1-3. C 1-4. C +Q Q C Q 1-5. ɛ 0 E 2 /

4 2 z = 0 ɛ 0 µ 0 ɛ µ x E D H B divd = 0 divb = 0 rote = B t roth = D t ε, 0 μ 0 ε, μ z 2-1. E E(r, t) = E 0 cos(k r ωt) B B(r, t) = k E 0cos(k r ωt) ω k ω 2-2. D t B t E H 2-3. x E x ɛ µ v 2-4. E 0 E T E R E R /E 0 ɛ 0 µ 0 ɛ µ ɛ = 9ɛ 0 µ = µ S = E H S 0 S T S R E 0

5 III 1 a 1 U (x) m U { 0 0 x a U(x)= 0 x=a x ^x ^p n h^xi h^pi Ψ(x) =Ax(a x) 1-4. A 1-5. Z ß 0 t 2 sin tdt = ß 2 4

6 2 m! 1 H = μh2 2m d 2 dx m!2 x 2 (1) (1) x d μh m! dx H(x; ) H(x; )ψ n (x; ) =E n ( )ψ n (x; ) (2) ψ n (x; ) n E n ( ) 2-1. (2) hψ n ψ n(x; )i f (x) g(x) hf (x)jg(x)i Z +1 (f (x)) Λ g(x) dx 1 ) hψ n (x; jψ n (x; )i n( ! μh (1) 1 1 n ht i hv i E n =(n + 1 )μh! 2

7 1 (2) x r R R C E n (R) ψ n (r; R) (3) H(r; R)ψ n (r; R) =E n (R)ψ n (r; R) (3) C ψ n (r;r+dl) R+dl dl R ψ n (r;r) 2-4. C R; R + dl ψ n (r; R); ψ n (r; R + dl) 2 dffi dffi Arghψ n (r; R)fi ψn (r; R + dl)i Arg dl 1 dffi dffi = ihψ n ψ n(r; R)i dl 2-5. dffi C fl n (C) fl n (C) = I C dffi = I C ihψ n ψ n(r; R)i dl ψ n (r; R) ψ ~ n (r; R) = e iffn(r) ψ n (r; R) ff n (R) 1

8 IV 1 2 A B t 0 A B T A =3T 0 T B = T 0 A V A T A B V B T B t t 0 A B V A /V B A B T A T B t T V 1 S S = N A k B ( 3 ln T +lnv )+. 2 N A k B t t 0

9 2 T V N ε p ε = pc c p p + dp 4πV p 2 dp/h 3 (h ) ln N! N ln N 2-1. Z Z = [ (kb T c ) ] 3 N 8πV h 3 N k B C V 2-4. S 2-5. E (E E ) 2 (E E ) 2 = k B T 2 C V

10 V 1 f(x) ω F (ω) = 1-1. f(x) f(x)e iωx dx f(x) = e ax2 a a > 0 F (ω) f(x) = e ax2 e ax2 dx = π a f(x) F (ω) 1-4. f(x) f(x) = 1 2 2π e 1 8 x2 F (ω) 1/e 2 φ A 2-1. (φa) = ( φ) A 2-2. C S (n φ) ds = S C φ dr n S ds r A, B, C A (B C) = B (C A) = C (A B)

11 3 z O 1 + i C 1, C 2, C 3 Im z 1 1+i O C 3 π 4 C 2 C Re z 3-1. I k = z dz C k k = 1, 2, 3 I 1, I 2, I I 1, I 2, I 3

12 VI 1 p p + dp n(p)dpp 0 { 8πp 2 n(p)dp = h dp (p p 3 0 ) 0 (p > p 0 ) h P v P = vpn(p)dp 1-1. n e p ρ µ e n e ρm u 1-3. p = m e v (m e ) v = c (c ) ρ 1-4. P = Kρ 1+1/n (K n ) 1 < n < 3 M RR 3 n 1/M n 1 n = 3

13 2 r = (x y z) (θ φ)i ν (r; θ φ) r dσ (θ φ)dω ν ν + dν I ν dν cos θdσdω θ dσφ ()F ν I ν F ν (r) = I ν (r; θ φ) cos θdω κ ν, ɛ ν si ν di ν (s) ds = κ ν (s)i ν (s) + ɛ ν (s) 2-1. τ ν (s) = s 0 κ ν(s )ds di ν dτ ν = I ν + S ν S ν S ν = ɛ ν /κ ν 2-2. (τ ν I ν ) τ ν = 0 I(0) 2-3. T S ν B ν (T ) TR τ ν 2-4. O b(< R) P P OP A B OA PAθ AB τ ν θa I ν (θ) 2-5. A F ν

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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)