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- みいか やなぎしま
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2 i
3 3.1.1 (Sr 0.6 K 0.4 )Fe 2 As Ba(Fe 0.93 Co 0.07 ) 2 As ii
4 (Kamerlingh Onnes) K 0 (superconductivity) 1957 BCS 0 (T c ) T c 4.2 K T c 1930 T c 1986 (Johannes G. Bednorz) (Karl Alex Müller) 30 K T c 1987 T c (77 K) T c 100 K T c 0 J c J c 2001 T c (39 K) MgB
5 LaOFeP 4 K [1] LaOFeP 2007 Fe Ni LaONiP [2] T c 4 K LaOFeP P As LaOFeAs F 26 K T c 2008 [3] T c La Sm SmO 1 x F x FeAs T c 50 K [4] REOFeAs 1111 AFe 2 As FeSe FeTe 11 LiFeAs 111 RE(Rare Earth) A FeAs REO A FeAs Li 122 F O REO CaF CaFeAsF Fe Co T c J c 2
6 1.3 [5, 6] J cl J cl (Sr 0.6 K 0.4 )Fe 2 As J cl (Sr 0.6 K 0.4 )Fe 2 As 2 SEM µ σ wt% SEM 1.2 SEM µ σ 1.5 J c Lorentz 3
7 1.1 (Sr 0.6 K 0.4 )Fe 2 As 2 SEM 20 wt% 1.2 ( SEM ξ 1.3 (a) 1.3 (b) Lorentz 4
8 2ξ nomal core nomal particle ( a) ( b) 1.3 (a) (b) Bc 2 /2µ 0 B c F p J c B J c [7] Ba(Fe 0.93 Co 0.07 ) 2 As c f p r 0 c t a-b 5
9 ξ ab f p π 4µ 0 B c 2 ξ ab t; ξ ab < r 0 π 4µ 0 B c 2 r 0 t; ξ ab r 0 (1.1) N p B ϕ ϕ 0 c t N p = B ϕ /tϕ 0 N p N p B B/ϕ 0 π (r 0 + ξ ab ) 2 1 π (r 0 + ξ ab ) 2 B/ϕ 0 N p N p = π (r 0 + ξ ab ) 2 BB ϕ tϕ 0 2 (1.2) F p0 F p0 = J c0 B = ηn pf p (1.3) η 1.4 short range G (0) = 1 4πL [ ( ) 1 4πBC11 log ( )] 4πBC66 log + 1 2C 11 α L ϕ 0 2C 66 α L ϕ 0 (1.4) C 11 C 66 α L Labusch C 11 C 66 α L ϕ 0 /4πB C 66 (1.4) G (0) B 2α L ϕ 0 L k 1 f (1.5) 6
10 1.4 k f long range K Campbell λ 0 K α L a f Lλ 0 (1.6) a f k 1 f = k 1 f + K 1 (1.7) k f /K a f /λ 0 1 k f k f 1.5 ( f p 1 4x f(x) = a f f p ( 4x a f 3 ) ; 0 x < a f 2 ) ; a f 2 x < a f (1.8) Campbell N f p f pt pf p ; f p > f pt F p0 = f p + f pt (1.9) 0; f p < f pt 7
11 1.5 campbell f pt = k f a f /4 f p (1.3) (1.9) η f pt /f p s = ϕ 0 /π 2 r 0 2 B ϕ η = 1 f pt/f p 1 + f pt /f p (1.10) f pt f p = (s + 1) + s2 + 6s + 1 2s < 1 (1.11) (1.11) J c0 = ηπ2 R 3 B ϕ B c 2 4µ 0 (1.12) R 3 R 3 = { r0 (r 0 + ξ ab ) 2 ; ξ ab > r 0 ξ ab (r 0 + ξ ab ) 2 ; ξ ab < r 0 (1.13) 8
12 (1.12) J c0 (1.12) η Campbell η η 1.7 U Lorentz 1.6 A Lorentz Lorentz U U 0 A B Lorentz Arrhenius exp( U/k B T ) (k B Boltzmann ) 1 a C a f a a f ν 0 ( E = Ba f ν 0 [exp U ) exp ( U )] k B T k B T (1.14) 9
13 1.6 U U Lorentz x 1.6 F (x) = U 0 sinkx fx (1.15) 2 k = 2π/a f V f = JBV Lorentz (1.15) x x = 1 ( ) 2f k cos 1 x 0 (1.16) U 0 k F (x) x = x 0 U = F (x 0 ) F ( x 0 ) [ ( ) ] 2 1/2 ( ) ( ) U 2f 2f 2f = 1 cos 1 U 0 U 0 k U 0 k U 0 k (1.17) U = 0 x 0 = 0 2f/U 0 k = 1 J 10
14 J c0 ( ) 2f = J j (1.18) U 0 k J c0 (1.17) U(j) = U 0 [(1 j 2 ) 1/2 jcos 1 j] (1.19) U U + fa f = U + πu 0 J J c0 (1.20) (1.14) [ E cr = Ba f ν 0 exp U(j) ] [ ( 1 exp πu )] 0j k B T k B T (1.21) j > 1 [ Ba f ν 0 exp U(j) ] [ ( 1 exp πu )] 0j ; j < 1 k B T k B T E cr = Ba f ν 0 [1 exp ( πu 0 k B T )] ; j 1 (1.22) E ff = { 0; j < 1 ρ f (J J c0 ); j 1 (1.23) ρ f E = (Ecr 2 + Eff) 2 1/2 (1.24) j < 1 j 1 11
15 J c0 [ ( T J c0 = ABc2(0) m 1 T c ) 2 ] m B γ 1 ( 1 B B c2 ) σ (1.25) AB m c2(0) m γ σ N p A f(a) = K exp [ (log A log A m) 2 ] 2σ 2 (1.26) K σ 2 A m A A E(J) = 0 Ef(A)dA (1.27) U 0 U 0 Û0 V U 0 = Û0V (1.28) Û0 Labusch α L d i Û 0 = α Ld 2 i 2 d i a f d i = a f ζ (1.29) (1.30) 12
16 L L d R ( a) d > L R ( b) d < L 1.7 L d (a) (b) ζ ζ = 2π J c0 α L d i J c0 B = α L d i (1.31) U 0 = 1 2ζ J c0ba f V (1.32) (1.32) V U 0 1.7(a) L R L L = ( C44 C 44 α L V = LR 2 (1.33) ) 1/2 ( ) 1/2 Baf = (1.34) ζµ 0 J c0 C 44 = B2 µ 0 (1.35) 13
17 R R = ( C66 α L ) 1/2 (1.36) C 66 3 C 66 = B2 c B 4µ 0 B c2 ( 1 B B c2 ) 2 C 0 66 (1.37) R a f R = ga f (1.38) g 2 [8] g 2 (1.36) (1.38) g 2 = C 66 ζj c0 Ba f (1.39) V (1.33) V = a f 2 g 2 L (1.40) (1.32) (1.40) g 2 U 0 (1.32) (1.33) (1.34) (1.38) U 0 = 1 2ζ J c0ba f LR 2 (1.41) U 0 = J 1/2 c0 B3/2 a 7/2 f g 2 2ζ 3/2 µ 1/2 0 (1.42) a f = ( 2ϕ0 3B ) 1/2 U 0 = 0.835g2 k B J 1/2 c0 (1.43) ζ 3/2 B 1/4 14
18 1.7(b) L d V = dr 2 (1.44) U 0 = 4.23g2 k B J c0 d ζb 1/2 (1.45) 1.8 T c (Sr 0.6 K 0.4 )Fe 2 As 2 10, 20wt% T c J cg J clt Ba(Fe 0.93 Co 0.07 ) 2 As 2 η 15
19 (Sr 0.6 K 0.4 )Fe 2 As 2 T c 34 K SEM µ 0.3 µm 1.0 µm H e l w (l > w) H m 0 T x y z z 2.1 xy Bean-London x 16
![2.1: sample w l t T c µ σ [mm] [mm] [mm] [K] [µm] (Sr 0.6 K 0.4 )Fe 2 As 2 1.12 1.73 0.75 34.3 0.3 0.70 (Sr 0.6 K 0.4 )Fe 2 As 2 +10 wt%ag 3.53 3.53 1.16 1.0 0.55 (Sr 0.](/docs-images/94/119024223/images/20-0.jpg "6 K 0.4 )Fe 2 As 2 +20 wt%ag 1.91 2.77 0.95 34.4 1.0 0.55 2.1: x+dx 2.2 z dz di c = J c dxdz (2.1) 2.2 S 1 S 1 = 2x2y = 4x(x + l w ) 2 = 4x 2 + 2x(l w) (2.")
20 2.1: sample w l t T c µ σ [mm] [mm] [mm] [K] [µm] (Sr 0.6 K 0.4 )Fe 2 As (Sr 0.6 K 0.4 )Fe 2 As wt%ag (Sr 0.6 K 0.4 )Fe 2 As wt%ag : x+dx 2.2 z dz di c = J c dxdz (2.1) 2.2 S 1 S 1 = 2x2y = 4x(x + l w ) 2 = 4x 2 + 2x(l w) (2.2) dm=s 1 di c 17
21 2.2: dx H p H m >2H p m = dm = S 1 (x)j c dxdz = J c t S 1 (x)dx (2.3) t H m < H p H p < H m <2H p m g m g = t 2J cg t J 2 cg ( w + l 2H ) m H J m; 2 cg Hm 3 (w + l)t Hm 2 + lwth m + w3 3lw 2 tj cg ; 2J cg 12 0 < H m < H p H p < H m < 2H p (3l w)w 2 tj cg ; H m > 2H p 12 J cg (2.4) R r r+dr 2.3 di c = J c rdrdθ (2.5) 18
22 2.3: dr S 2 S 2 = π(r sin θ) 2 (2.6) dm=s 2 di c m l m l = π 2 ( 3R 2 Hm 2 8 J cl ( π 2 8 6RH3 m J 2 cl R 4 J cl + 4R 3 H m 3R2 H 2 m J cl ) + 7H4 m 8Jcl 3 ; 0 < H m < H p + RH3 m J 2 cl ) H4 m 8Jcl 3 ; H p < H m < 2H p (2.7) R 4 π 2 J cl ; H m > 2H p 8 J cl [9] R µ/2 J clt SQUID m [emu] SI m[am 2 ] = m[emu] 10 3 (2.8) 19
23 2.1.3 T c 0 T (m R ) T 1 T K 25 K 5 K 2.4 m R H m m R H m 2.5 (w + l)h p /3w ( )H p /7 H p J cg, J cl J cg = 2H pg w J cl = H pl R (2.9) H p H pg H pl R µ/2 J cl R P (R) = 1 2 (log R log µ)2 exp πσ R 2σ 2 (2.10) µ σ m l m l(h m ) = 0 m(r, H m )P (R)dR (2.11) dm l /dh m H pl H pl J clt m R m l m g m R = m l N l + m g (2.12) 20
24 6 m R H p 2H p H m 2.4: m R -H m 0.6 dm R /dh m H p 2H p H m 2.5: m R H m (w + l)h p /3w, ( )Hp /7 21
25 N l m l m g m l = R4 π 2 8 J clt m g = (3l w)w2 t J cg (2.13) 12 N l F V g V l N l = V g V l F (2.14) K K = (bf )2 F 2 c 1 F 2 c = J cg J clt (2.15) [10] b F c = K 5 K 25 K 5 K 5 J cg J clt Ba(Fe 0.93 Co 0.07 ) 2 As 2 JAEA Au c 200 MeV NIRS HIMAC Xe c 800 MeV B ϕ 2 T 2 T 16 T T c 24 K 2.6 Au Ba(Fe 0.93 Co 0.07 ) 2 As 2 TEM 22
![2.6 Au Ba(Fe 0.93 Co 0.07 ) 2 As 2 2 T, 200 MeV [11] 2.2.2 7 T 0 T 7 T 7 T 0 T m m = (3l w) w2 t J c (2.](/docs-images/94/119024223/images/26-0.jpg "16) 6 J c B (1.25) J c0 (1.12) 2.2.3 η η η 23")
26 2.6 Au Ba(Fe 0.93 Co 0.07 ) 2 As 2 2 T, 200 MeV [11] T 0 T 7 T 7 T 0 T m m = (3l w) w2 t J c (2.16) 6 J c B (1.25) J c0 (1.12) η η η 23
27 k f k f 2.8 x y 500 nm 500 nm x 2 η F p U F p = ( ) U x MAX (2.17) 24
28 2.8 2 η (1.3) η = F P N pf P (2.18) N p f p (1.35) (1.1) (1.2) η f pt /f p η (1.10) f pt /f p s = ϕ 0 /π 2 r 0 2 B ϕ (1.11) B ϕ r 0 ξ ab, k f η 25
29 (Sr 0.6 K 0.4 )Fe 2 As 2 (Sr 0.6 K 0.4 )Fe 2 As 2 3.1(a), (b) 20 wt% (2.10) µ σ wt% SEM 20 wt% σ 3.2 (2.11) σ dm l /dh m H m J cl = A/m 2 µ = m σ J cl 3.2 σ J cl J clt σ R 4 m l 3.3 J clt /J cl σ σ < 0.1 J cl J clt σ > 0.1 J clt /J cl σ = 1 J cl 10 26
30 3.1: (Sr 0.6 K 0.4 )Fe 2 As 2 (2.10) (a) (b) 20 wt% [ ] 4 =0.70 dm l /dh m 2 = = H m [A/m] 3.2: σ dm l/dh m -H m σ J cl J clt 27
31 10 0 J clt /J cl 10 1 #2 ( =0.55) #1 ( =0.70) : J clt /J cl -σ σ < 0.1 σ > 0.1 J clt /J cl 3.4 (2.4), (2.7) (Sr 0.6 K 0.4 )Fe 2 As 2 J cg 0 10, 20 wt% 5 K 10 7 A/m 2, 10 7 A/m 2 J clt 5 K A/m 2 10, 20 wt% A/m 2, A/m 2 J clt J cg J clt σ > 0.1 σ <
32 10 10 J c [A/m 2 ] 10 8 J clt J cg pure 10Ag 20Ag T[K] 3.4: (Sr 0.6 K 0.4 )Fe 2 As 2 J cg 0 10 wt% 20 wt% J clt J clt J cg (Sr 0.6 K 0.4 )Fe 2 As 2 F (2.12) (2.13) m g, m l (2.14) F 10, 20 wt% F 0.21, 0.69, 0.46 F c = J cg 29
33 (2.15) 10, 20 wt% K 0.49, 0.11 F c K J cg J ct 2 10 J cg J clt K J cg /J clt 10, 20 wt% K , F 10, 20 wt% 0.31, 0.32 F c F F c J cg Ba(Fe 0.93 Co 0.07 ) 2 As 2 Ba(Fe 0.93 Co 0.07 ) 2 As 2 Au 40% nm 2 5 nm Au J c 3.5(a) Xe, U J c 3.5(b) 3.5(a) Au J c 2 K A/m 2 6 [11] 3.5(b) 2 K Xe A/m 2, U 2 T A/m 2, 16 T A/m Au [7] -123 Bi-2212 Bi
34 3.5: Ba(Fe 0.93 Co 0.07 ) 2 As 2 (a) Au (b) Xe 2 T U 2, 16 T Au J c B c 2 / 2µ0 (J/m 3 ) 10 4 Ba(Fe 0.93 Co 0.07 ) 2 As 2 (Au irradiation) Y 123 Bi 2212 Bi 2223 Dy T / T c 3.6: Ba(Fe 0.93 Co 0.07 ) 2 As Bi-2212 Bi
35 3.1: ion Au Xe U(B ϕ =2 T) U(B ϕ =16 T) r 0 [nm] Xe, U r U B ϕ 2 T 16 T r f pt /f p η f pt /f p (1.11) B ϕ 3.8(a) r 0 3.8(b) B ϕ = 2 T, ξ ab = 3 nm, r 0 = 3 nm η 3.8(a) B ϕ f pt /f p 10 1 η B ϕ 7 T (b) r 0 f pt /f p 10 2 η 3.11 r 0 3.8(a), (b) ξ ab k f η 3.9 ξ ab η 3.9(a) k f B η 3.9(b) 3.9(a) 32
36 3.7: B ϕ ξ ab 0.6 η 3.8(b) r 0 ξ ab 3.0 η 3.12 ξ ab 3.9(b) k f η 3.9(a), (b) k f B η ξ ab r 0 = 3 η ξ ab 33
37 3.8: f pt /f p η (a) B ϕ f pt /f p 10 1 η (b) r 0 f pt /f p 10 2 η 3.9: ξ ab k f η (a) ξ ab ξ ab η (b) B k f k f η 34
38 3.10: B ϕ 3.11: r 0 r 0 35
39 3.12: ξ ab ξ ab 36
40 4 (Sr 0.6 K 0.4 )Fe 2 As 2 Au Ba(Fe 0.93 Co 0.07 ) 2 As 2 Xe, U (Sr 0.6 K 0.4 )Fe 2 As 2 37
41 (Sr 0.6 K 0.4 )Fe 2 As 2 J cg Ba(Fe 0.93 Co 0.07 ) 2 As 2 Au 6 Xe U Ba(Fe 0.93 Co 0.07 ) 2 As Bi Bi Xe, U 38
42 39
43 40
44 [1] Y. Kamihara, H. Hiramatsu, M. Hirano, R. Kawamura, H. Yanagi, T. Kamiya, H. Hosono, J. Am. Chem. Soc., 128 (2006) [2] T. Watanabe, H. Yanagi, T. Kamiya, Y. Kamihara, H. Hiramatsu, M. Hirano, H. Hosono, Inorg. Chem., 46 (2007) [3] Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, J. Am. Chem. Soc., 130 (2008) [4] Z. Ren, W. Lu, J. Yang, W. Yi, X. Shen, Z. Li, G. Che, X. Dong, L. Sun, F. Zhou, Z. Zhao, Chin. P hys. Lett. 25 (2008) [5] A. Yamamoto, A. A. Polyanskii, J. Jiang, F. Kametani, C. Tarantini, F. Hunte, J. Jaroszynski, E. E. Hellstrom, P. J. Lee, A. Gurevich, D. C. Larbalestier, Z. A. Ren, J. Yang, X. L. Dong, W. Lu, Z. X. Zhao, Supercond. Sci. T echnol. 21 (2008) [6] E. S. Otabe, M. Kiuchi, S. Kawai, Y. Morita, J. Geb, B. Ni, Z. Gao, L. Wang, Y. Qi, X. Zhang, Y. Ma, P hysica C 469 (2009) [7] E. S. Otabe, I. Kohno, M. Kiuchi, T. Matsushita, T. Nomura, T. Motohashi, M. Karppinen, H. Yamauchi, S. Okayasu, Adv. Cryo. Eng. 52 (2006) [8] T. Matsushita, P hysica C 217 (1993) 461. [9] K. Murakami, T. Mayumi, M. Kiuchi, E. S. Otabe, T. Matsushita, J. Ge, B. Ni, L. Wang, Y. Qi, X. Zhang, Z. Gao, Y. Ma, P hysica C 471 (2011) [10] D. W. Heermann, D. Stauffer, Z. P hysik B 44 (1981) 339. [11] Y. Nakajima, Y. Tsuchiya, T. Taen, T. Tamegai, S. Okayasu, M. Sasase, P hys. Rev. B 80 (2009)
BaHfO 3 PLD GdBa 2 Cu 3 O 7 δ 24 2 17 1 1 1.1.................................. 1 1.2............................... 2 1.3............................. 2 1.4................................. 3 1.5.........................
Ni PLD GdBa 2 Cu 3 O 7 x 2 6
Ni PLD GdBa 2 Cu 3 O 7 x 2 6 1 1 1.1.................................. 1 1.2................................ 2 1.2.1......................... 3 1.3 RE 1 Ba 2 Cu 3 O 7 x...................... 3 1.3.1...............................
BaHfO 3 PLD GdBa 2 Cu 3 O x 25 2 6 1 1 1.1.................................. 1 1.2....................... 3 1.2.1............................ 3 1.2.2.............................. 5 1.2.3.........................
MgB 2 Mg B
MgB 2 Mg B 23 2 22 1 1 1.1..................................... 1 1.2.............................. 4 1.3.................................. 5 1.4................................... 5 1.5.....................................
() x + y + y + x dy dx = 0 () dy + xy = x dx y + x y ( 5) ( s55906) 0.7. (). 5 (). ( 6) ( s6590) 0.8 m n. 0.9 n n A. ( 6) ( s6590) f A (λ) = det(a λi)
0. A A = 4 IC () det A () A () x + y + z = x y z X Y Z = A x y z ( 5) ( s5590) 0. a + b + c b c () a a + b + c c a b a + b + c 0 a b c () a 0 c b b c 0 a c b a 0 0. A A = 7 5 4 5 0 ( 5) ( s5590) () A ()
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)
II 2 II
II 2 II 2005 yugami@cc.utsunomiya-u.ac.jp 2005 4 1 1 2 5 2.1.................................... 5 2.2................................. 6 2.3............................. 6 2.4.................................
6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m f 4
35-8585 7 8 1 I I 1 1.1 6kg 1m P σ σ P 1 l l λ λ l 1.m 1 6kg 1.1m 1.m.1m.1 l λ ϵ λ l + λ l l l dl dl + dλ ϵ dλ dl dl + dλ dl dl 3 1. JIS 1 6kg 1% 66kg 1 13 σ a1 σ m σ a1 σ m σ m σ a1 f f σ a1 σ a1 σ m
W u = u(x, t) u tt = a 2 u xx, a > 0 (1) D := {(x, t) : 0 x l, t 0} u (0, t) = 0, u (l, t) = 0, t 0 (2)
3 215 4 27 1 1 u u(x, t) u tt a 2 u xx, a > (1) D : {(x, t) : x, t } u (, t), u (, t), t (2) u(x, ) f(x), u(x, ) t 2, x (3) u(x, t) X(x)T (t) u (1) 1 T (t) a 2 T (t) X (x) X(x) α (2) T (t) αa 2 T (t) (4)
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Contents a 6 6 6 6 6 6 6 7 7. 8.. 8.. 8.3. 8 Part. 9. 9.. 9.. 3. 3.. 3.. 3 4. 5 4.. 5 4.. 9 4.3. 3 Part. 6 5. () 6 5.. () 7 5.. 9 5.3. Γ 3 6. 3 6.. 3 6.. 3 6.3. 33 Part 3. 34 7. 34 7.. 34 7.. 34 8. 35
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
) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4
![) ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4](/thumbs/92/107866707.jpg ") ] [ h m x + y + + V x) φ = Eφ 1) z E = i h t 13) x << 1) N n n= = N N + 1) 14) N n n= = N N + 1)N + 1) 6 15) N n 3 n= = 1 4 N N + 1) 16) N n 4")
1. k λ ν ω T v p v g k = π λ ω = πν = π T v p = λν = ω k v g = dω dk 1) ) 3) 4). p = hk = h λ 5) E = hν = hω 6) h = h π 7) h =6.6618 1 34 J sec) hc=197.3 MeV fm = 197.3 kev pm= 197.3 ev nm = 1.97 1 3 ev
x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x
[ ] IC. f(x) = e x () f(x) f (x) () lim f(x) lim f(x) x + x (3) lim f(x) lim f(x) x + x (4) y = f(x) ( ) ( s46). < a < () a () lim a log xdx a log xdx ( ) n (3) lim log k log n n n k=.3 z = log(x + y ),
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1906 R n m 1 = =1 1 R R= 8h ICP s p s HeNeArXe 1 ns 1 1 1 1 1 17 NaCl 1.3 nm 10nm 3s CuAuAg NaCl CaF - - HeNeAr 1.7(b) 2 2 2d = a + a = 2a d = 2a 2 1 1 N = 8 + 6 = 4 8 2 4 4 2a 3 4 π N πr 3 3 4 ρ = = =
meiji_resume_1.PDF
β β β (q 1,q,..., q n ; p 1, p,..., p n ) H(q 1,q,..., q n ; p 1, p,..., p n ) Hψ = εψ ε k = k +1/ ε k = k(k 1) (x, y, z; p x, p y, p z ) (r; p r ), (θ; p θ ), (ϕ; p ϕ ) ε k = 1/ k p i dq i E total = E
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
![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](/thumbs/101/149159646.jpg "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")
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
Chap11.dvi
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