7) ẋt) =iaω expiωt) ibω exp iωt) 9) ẋ0) = iωa b) = 0 0) a = b a = b = A/ xt) = A expiωt) + exp iωt)) = A cosωt) ) ) vt) = Aω sinωt) ) ) 9) ) 9) E = mv
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1 - - m k F = kx ) kxt) =m d xt) dt ) ω = k/m ) ) d dt + ω xt) = 0 3) ) ) d d dt iω dt + iω xt) = 0 4) ω d/dt iω) d/dt + iω) 4) ) d dt iω xt) = 0 5) ) d dt + iω xt) = 0 6) 5) 6) a expiωt) b exp iωt) ) ) xt) =a expiωt)+b exp iωt) 7) a b t =0 x0) = A v0) = ẋ0) = 0 7) x0) = a + b = A 8)
2 7) ẋt) =iaω expiωt) ibω exp iωt) 9) ẋ0) = iωa b) = 0 0) a = b a = b = A/ xt) = A expiωt) + exp iωt)) = A cosωt) ) ) vt) = Aω sinωt) ) ) 9) ) 9) E = mv + mω x 3) E = m [ Aω sinωt)] + mω [A cosωt)] = mω A 4) V x) = kx = mω x 5) F = dv/ F = kx V = kx / ) V x) p i h Ψx, t) =Ĥˆp, x)ψx, t) 6) t Ĥˆp, x) = h + V x) 7) m x Hp, x) = p + V x) 8) m ˆp = i h x 9)
![Aω sinωt)] + mω [A cosωt)] = mω A 4) V x) = kx = mω x 5) F = dv/ F = kx V = kx / ) V x)](/docs-images/43/20606897/images/page_2.jpg "p i h Ψx, t) =Ĥˆp, x)ψx, t) 6) t Ĥˆp, x) = h + V x) 7) m x Hp, x) = p + V x) 8) m ˆp =")
3 Ψx, t) Ψx, t) t x 5) i h [ t Ψx, t) = h m x + ] mω x Ψx, t) 0) t x Ψx, t) =ux)vt) ux)vt) i h vt) /vt) = [ h t m x + ] mω x ux)/ux) ) At) =Bx) x t At) =Bx) = ɛ ) i h dvt) dt [ h d m + mω x ) = ɛvt) ) ] ux) =ɛux) 3) vt) =v0) exp iɛt h ) 4) 3
4 3). mω X = h x 5) X ω [T ] h [LMLT ] [MT /M L T ] / =[L ] X h/mω 3) mω x = hω X d = mω d h 6) hω ) d + X ux) =ɛux) 7) d / + X X d ) ) ) d d + X + X + X d ) + X 8) B = d ) + X 9) ) d B = + X 30) 8) B B = d ) ) d + X + X = d d X + X d + X 3) d/)x + Xd/) d/)x = 3) ux) B B fx) d X + X d ) fx) = xfx) + X df X) = X df X) fx)+x df X) = fx) 3) 4
5 fx) d X + X d = 33) 30) 33) ) B B = d + X 34) BB ) BB = d + X + 35) BB B B = 36) 7 X Ĥ = hω ) d + X B,B 34) Ĥ = hω B B + ) 37) 38) 7 ux) B,B ux) 7 B ux) BuX) 7 7 BuX) BuX) =u X) Ĥu X) = hω B B + ) BuX) = hω B BBuX)+ ) BuX) 39) hω B B + ) ux) =ɛux) 40) hωb BuX) = ɛ hω ) ux) 4) 36) Ĥu X) =ɛ hω)u X) 4) 5
6 36) B B = BB B B)B =BB )B = BB B) B 43) 4) Ĥu X) = hω B B)B + ) B ux) = hω BB B) B + ) B ux) = B [ hω B B + ) hω ] ux) = Bɛ hω)ux) = ɛ hω)u X) 44) 4) B ux) B n ux) 40) ux) ɛ Ĥ ux) u X) Ĥu X) =ɛ hω)u X) 45) 4) B n ux) u n X) ĤBu X) =ɛ hω hω)bu X) 46) Ĥu n X) =ɛ n hω)u n X) 47) ɛ n = ɛ n hω n E = p m + mω x 48) E>0 n ɛ n > 0 ɛ 0 u 0 X) ɛ 0 Ĥu 0 X) =ɛ 0 u 0 X) 49) Bu 0 X) = 0 50) 6
7 Bu 0 X) 0 ĤBu 0 X) =ɛ 0 hω)bu 0 X) 5) ɛ 0 hω Bu 0 X) 50) u 0 X) u 0 X) B B = d/ + X)/ 50) du 0 X) + Xu 0X) = 0 5) B B 50) 5) du 0 X)/ u 0X) = X 53) log u 0 X) = X + 54) u 0 X) =C 0 exp X ) 55) C 0 C 0 B B u 0 X) 38) 50) Bu 0 =0 Ĥu 0 X) = hωb Bu 0 X)+ hωu 0X) 56) Ĥu 0 X) = hωu 0X) 57) ɛ 0 = hω n 4) 57) B B Ĥu 0 X) =ɛ 0 B u 0 X) 58) 7
8 B Ĥ = hωb B B + B ) = hω[b BB ) + B ) = hωb B + )B = Ĥ hω)b 58) ĤB u 0 X) = hω + ɛ 0 )B u 0 X) 59) C B 3 u 0 X) =u X) ɛ = hω + ɛ 0 = hω Ĥu X) =ɛ u X) 60) u X) ɛ hω 57) 60) 0 Ĥu X) =ɛ u X) 6) u X) =C B u X) =C C B ) u 0 X) 6) ɛ = ɛ + hω = hω + ) 63) Ĥu n X) =ɛ n u n X)n =0,,, ) 64) n u n X) =C n B u n X) = C m B ) n u 0 X) 65) m= ɛ n = ɛ n + hω = hωn + ) 66) u,u,u 3, 65) B u 0 X) u n X) = n n! X d ) n exp x π ) 67) u X) = C 0C X u X) = C X u 3 X) = d ) exp x )= π X) exp x ) 68) d ) u X) =! π 4X ) exp x ) 69) 3 3! π 8X 3 X) exp x ) 70) n 8
9 . H n x) u n X) exp x /) X H n x) = ) n expx ) dn n exp x ) 7) H 0 x) = ) 0 expx ) exp x ) = 7) H x) = ) expx ) d exp x )=x 73) H x) = ) expx ) d x exp x ) ) =4x 74) u 0,u,u u n X) u n X) = n n! π H nx) exp x ) 75) 67) x d = ) expx ) d exp x ) 76) 76) fx) ) exp x ) d ] ] [exp x )fx) = ) exp [ x) x ) exp x x) df x) )fx) + exp x )df = xfx) 77) 76) 76) x d ) n = ) n exp x ) dn n exp x ) 78) u n x) x d ) n exp x )= )n exp x ) dn = exp x ) n exp x ) exp x ) ] [ ) n expx ) dn n exp x ) = exp x )H nx) 79) 67) 75) u n X) H n X) 9
![π H nx) exp x ) 75) 67) x d = ) expx ) d exp x ) 76) 76) fx) ) exp x ) d ] ] [exp x )fx) = ) exp [ x) x ) exp x x) df x) )fx) + exp](/docs-images/43/20606897/images/page_9.jpg "x )df = xfx) 77) 76) 76) x d ) n = ) n exp x ) dn n exp x ) 78) u n x) x d ) n exp x )= )n exp x ) dn = exp x ) n exp x ) exp x ) ]")
10 .3 d H nx) x d H nx)+nh n x) = 0 80) n m, H m x)h n x)e x = 0 8) exp x ) H n H n = [H n x)] e x = n n! π 8) 8) u n x).4 Gx, t) Gx, t) t Gx, t) = expxt t ) 83) Gx, t) = n! H nx)t n 84) H n x) t n Gx, t) 84) H n x) 7) 84) expxt t ) = exp[ x t) ] expx ) exp[ x t) ] t x 84) Gx, t) = expx ) exp[ x t) ]= = n! n! [ d n exp t ] ) t) n t=x dt n [ ) n expx ) dn exp x ) n ] t n 85) 0
![H nx)t n 84) H n x) t n Gx, t) 84) H n x) 7) 84) expxt t ) = exp[ x t) ] expx ) exp[ x t) ] t](/docs-images/43/20606897/images/page_10.jpg "x 84) Gx, t) = expx ) exp[ x t) ]= = n!")
11 .5 d H nx) =nh n x) 86) n =,, 3, ) H n+ x) xh n x)+nh n x) = 0 87) n =,, 3, ) 87) H n x) 84) x Gx, t) x = n! dh n x) t n 88) Gx, t) x = x expxt t )=t expxt t ) =t n! H nx)t n = = m= n! H nx)t n+ m m! H m x)t m 89) 88) 89) t 87) 88) 84) t t expxt t )= x t) expxt t )= n! H nx)nt n n )! H nx)t n 90) t 88) 87) 88) 88) n nh n x) xn)h n x)+n[n )]H n x) = 0 9) 87) 80) d H nx) =n d H n x) =n[n )]H n x) 9)
12 d e x dh nx) ) +ne x H n x) = 0 93) exp x ) H m x) n m [ d H m x) e dh ) ] [ nx) d x +ne x H n x) H n x) e dh ) ]) mx) x +me x H m x) [ = H m x) d e dh )] [ nx) x H n x) d e dh )]) mx) x +n m) e x H m x)h n x) =0 94) [ H m x) d e dh )] [ nx) x = H m x)e dh ] nx) x dh mx) e dh nx) x 95) exp x ) n m) e x H m x)h n x) = 0 96) n m 8) 8) [H n x)] +n )H n x)h n x) H n+ x)h n x) n [H n x)] = 0 97) [H n x)] 88) H n x) [H n x)] xh n x)h n x) n )H n x)h n x) = 0 98) xh n x) 88) [H n x)] H n+ x)+nh n x))h n x) n )H n x)h n x) = 0 99) 97) 97) H n =n H n 00) 97) exp x ) e x [H n x)] +n ) e x H n+ x)h n x) n e x H n x)h n x) e x [H n x)] =0
![x) = 0 96) n m 8) 8) [H n x)] +n )H n x)h n x) H n+ x)h n x) n [H n x)] = 0 97) [H n x)] 88) H n x) [H n x)] xh n x)h n x) n )H n x)h n x) = 0 98) xh n x) 88)](/docs-images/43/20606897/images/page_12.jpg "[H n x)] H n+ x)+nh n x))h n x) n )H n x)h n x) = 0 99) 97) 97) H n =n H n 00) 97) exp x ) e x [H n x)] +n ) e x H n+ x)h n x) n e x H n x)h n x) e x [H n x)]")
13 00) 8) 00) H n = n H n = n n ) H n = = n n! H 0 = n n! π H 0 = H 0 = = e x [H 0 x)] e x = n n! π 8) 3
(3) (2),,. ( 20) ( s200103) 0.7 x C,, x 2 + y 2 + ax = 0 a.. D,. D, y C, C (x, y) (y 0) C m. (2) D y = y(x) (x ± y 0), (x, y) D, m, m = 1., D. (x 2 y
[ ] 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)
1.1 ft t 2 ft = t 2 ft+ t = t+ t 2 1.1 d t 2 t + t 2 t 2 = lim t 0 t = lim t 0 = lim t 0 t 2 + 2t t + t 2 t 2 t + t 2 t 2t t + t 2 t 2t + t = lim t 0
A c 2008 by Kuniaki Nakamitsu 1 1.1 t 2 sin t, cos t t ft t t vt t xt t + t xt + t xt + t xt t vt = xt + t xt t t t vt xt + t xt vt = lim t 0 t lim t 0 t 0 vt = dxt ft dft dft ft + t ft = lim t 0 t 1.1
r 1 m A r/m i) t ii) m i) t B(t; m) ( B(t; m) = A 1 + r ) mt m ii) B(t; m) ( B(t; m) = A 1 + r ) mt m { ( = A 1 + r ) m } rt r m n = m r m n B
1 1.1 1 r 1 m A r/m i) t ii) m i) t Bt; m) Bt; m) = A 1 + r ) mt m ii) Bt; m) Bt; m) = A 1 + r ) mt m { = A 1 + r ) m } rt r m n = m r m n Bt; m) Aert e lim 1 + 1 n 1.1) n!1 n) e a 1, a 2, a 3,... {a n
M3 x y f(x, y) (= x) (= y) x + y f(x, y) = x + y + *. f(x, y) π y f(x, y) x f(x + x, y) f(x, y) lim x x () f(x,y) x 3 -
M3............................................................................................ 3.3................................................... 3 6........................................... 6..........................................
f(x) = x (1) f (1) (2) f (2) f(x) x = a y y = f(x) f (a) y = f(x) A(a, f(a)) f(a + h) f(x) = A f(a) A x (3, 3) O a a + h x 1 f(x) x = a
3 3.1 3.1.1 A f(a + h) f(a) f(x) lim f(x) x = a h 0 h f(x) x = a f 0 (a) f 0 (a) = lim h!0 f(a + h) f(a) h = lim x!a f(x) f(a) x a a + h = x h = x a h 0 x a 3.1 f(x) = x x = 3 f 0 (3) f (3) = lim h 0 (
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211 ( 4 2 1. 3 1.1............................... 3 1.2 1- -......................... 13 1.3 2-1 -................... 19 1.4 3- -......................... 29 2. 37 2.1................................ 37
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
( ) ( ) ( ) i (i = 1, 2,, n) x( ) log(a i x + 1) a i > 0 t i (> 0) T i x i z n z = log(a i x i + 1) i=1 i t i ( ) x i t i (i = 1, 2, n) T n x i T i=1 z = n log(a i x i + 1) i=1 x i t i (i = 1, 2,, n) n
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
(1) (2) (3) (4) HB B ( ) (5) (6) (7) 40 (8) (9) (10)
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( ) ( 40 )+( 60 ) Schrödinger 3. (a) (b) (c) yoshioka/education-09.html pdf 1
2009 1 ( ) ( 40 )+( 60 ) 1 1. 2. Schrödinger 3. (a) (b) (c) http://goofy.phys.nara-wu.ac.jp/ yoshioka/education-09.html pdf 1 1. ( photon) ν λ = c ν (c = 3.0 108 /m : ) ɛ = hν (1) p = hν/c = h/λ (2) h
http://www.ike-dyn.ritsumei.ac.jp/ hyoo/wave.html 1 1, 5 3 1.1 1..................................... 3 1.2 5.1................................... 4 1.3.......................... 5 1.4 5.2, 5.3....................
211 kotaro@math.titech.ac.jp 1 R *1 n n R n *2 R n = {(x 1,..., x n ) x 1,..., x n R}. R R 2 R 3 R n R n R n D D R n *3 ) (x 1,..., x n ) f(x 1,..., x n ) f D *4 n 2 n = 1 ( ) 1 f D R n f : D R 1.1. (x,
1 180m g 10m/s 2 2 6 1 3 v 0 (t=0) z max t max t z = z max 1 2 g(t t max) 2 (6) 1.3 2 3 3 r = (x, y, z) e x, e y, e z r = xe x + ye y + ze z. (7) v =
1. 2. 3 3. 4. 5. 6. 7. 8. 9. I http://risu.lowtem.hokudai.ac.jp/ hidekazu/class.html 1 1.1 1 a = g, (1) v = g t + v 0, (2) z = 1 2 g t2 + v 0 t + z 0. (3) 1.2 v-t. z-t. z 1 z 0 = dz = v, t1 dv v(t), v
(, ) (, ) S = 2 = [, ] ( ) 2 ( ) 2 2 ( ) 3 2 ( ) 4 2 ( ) k 2,,, k =, 2, 3, 4 S 4 S 4 = ( ) 2 + ( ) ( ) (
![(, ) (, ) S = 2 = [, ] ( ) 2 ( ) 2 2 ( ) 3 2 ( ) 4 2 ( ) k 2,,, k =, 2, 3, 4 S 4 S 4 = ( ) 2 + ( ) ( ) (](/thumbs/92/107866524.jpg "(, ) (, ) S = 2 = [, ] ( ) 2 ( ) 2 2 ( ) 3 2 ( ) 4 2 ( ) k 2,,, k =, 2, 3, 4 S 4 S 4 = ( ) 2 + ( ) ( ) (")
B 4 4 4 52 4/ 9/ 3/3 6 9.. y = x 2 x x = (, ) (, ) S = 2 = 2 4 4 [, ] 4 4 4 ( ) 2 ( ) 2 2 ( ) 3 2 ( ) 4 2 ( ) k 2,,, 4 4 4 4 4 k =, 2, 3, 4 S 4 S 4 = ( ) 2 + ( ) 2 2 + ( ) 3 2 + ( 4 4 4 4 4 4 4 4 4 ( (
7 9 7..................................... 9 7................................ 3 7.3...................................... 3 A A. ω ν = ω/π E = hω. E
B 8.9.4, : : MIT I,II A.P. E.F.,, 993 I,,, 999, 7 I,II, 95 A A........................... A........................... 3.3 A.............................. 4.4....................................... 5 6..............................
d (K + U) = v [ma F(r)] = (2.4.4) t = t r(t ) = r t 1 r(t 1 ) = r 1 U(r 1 ) U(r ) = t1 t du t1 = t F(r(t)) dr(t) r1 = F dr (2.4.5) r F 2 F ( F) r A r
![d (K + U) = v [ma F(r)] = (2.4.4) t = t r(t ) = r t 1 r(t 1 ) = r 1 U(r 1 ) U(r ) = t1 t du t1 = t F(r(t)) dr(t) r1 = F dr (2.4.5) r F 2 F ( F) r A r](/thumbs/85/92098187.jpg "d (K + U) = v [ma F(r)] = (2.4.4) t = t r(t ) = r t 1 r(t 1 ) = r 1 U(r 1 ) U(r ) = t1 t du t1 = t F(r(t)) dr(t) r1 = F dr (2.4.5) r F 2 F ( F) r A r")
2.4 ( ) U(r) ( ) ( ) U F(r) = x, U y, U = U(r) (2.4.1) z 2 1 K = mv 2 /2 dk = d ( ) 1 2 mv2 = mv dv = v (ma) (2.4.2) ( ) U(r(t)) r(t) r(t) + dr(t) du du = U(r(t) + dr(t)) U(r(t)) = U x = U(r(t)) dr(t)
x i [, b], (i 0, 1, 2,, n),, [, b], [, b] [x 0, x 1 ] [x 1, x 2 ] [x n 1, x n ] ( 2 ). x 0 x 1 x 2 x 3 x n 1 x n b 2: [, b].,, (1) x 0, x 1, x 2,, x n
![x i [, b], (i 0, 1, 2,, n),, [, b], [, b] [x 0, x 1 ] [x 1, x 2 ] [x n 1, x n ] ( 2 ). x 0 x 1 x 2 x 3 x n 1 x n b 2: [, b].,, (1) x 0, x 1, x 2,, x n](/thumbs/92/108343288.jpg "x i [, b], (i 0, 1, 2,, n),, [, b], [, b] [x 0, x 1 ] [x 1, x 2 ] [x n 1, x n ] ( 2 ). x 0 x 1 x 2 x 3 x n 1 x n b 2: [, b].,, (1) x 0, x 1, x 2,, x n")
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30 I .............................................2........................................3................................................4.......................................... 2.5..........................................
I ( ) 1 de Broglie 1 (de Broglie) p λ k h Planck ( Js) p = h λ = k (1) h 2π : Dirac k B Boltzmann ( J/K) T U = 3 2 k BT
I (008 4 0 de Broglie (de Broglie p λ k h Planck ( 6.63 0 34 Js p = h λ = k ( h π : Dirac k B Boltzmann (.38 0 3 J/K T U = 3 k BT ( = λ m k B T h m = 0.067m 0 m 0 = 9. 0 3 kg GaAs( a T = 300 K 3 fg 07345
A A = a 41 a 42 a 43 a 44 A (7) 1 (3) A = M 12 = = a 41 (8) a 41 a 43 a 44 (3) n n A, B a i AB = A B ii aa
1 2 21 2 2 [ ] a 11 a 12 A = a 21 a 22 (1) A = a 11 a 22 a 12 a 21 (2) 3 3 n n A A = n ( 1) i+j a ij M ij i =1 n (3) j=1 M ij A i j (n 1) (n 1) 2-1 3 3 A A = a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33
m d2 x = kx αẋ α > 0 (3.5 dt2 ( de dt = d dt ( 1 2 mẋ kx2 = mẍẋ + kxẋ = (mẍ + kxẋ = αẋẋ = αẋ 2 < 0 (3.6 Joule Joule 1843 Joule ( A B (> A ( 3-2
3 3.1 ( 1 m d2 x(t dt 2 = kx(t k = (3.1 d 2 x dt 2 = ω2 x, ω = x(t = 0, ẋ(0 = v 0 k m (3.2 x = v 0 ω sin ωt (ẋ = v 0 cos ωt (3.3 E = 1 2 mẋ2 + 1 2 kx2 = 1 2 mv2 0 cos 2 ωt + 1 2 k v2 0 ω 2 sin2 ωt = 1
2.2 ( y = y(x ( (x 0, y 0 y (x 0 (y 0 = y(x 0 y = y(x ( y (x 0 = F (x 0, y(x 0 = F (x 0, y 0 (x 0, y 0 ( (x 0, y 0 F (x 0, y 0 xy (x, y (, F (x, y ( (
(. x y y x f y = f(x y x y = y(x y x y dx = d dx y(x = y (x = f (x y = y(x x ( (differential equation ( + y 2 dx + xy = 0 dx = xy + y 2 2 2 x y 2 F (x, y = xy + y 2 y = y(x x x xy(x = F (x, y(x + y(x 2
1 c Koichi Suga, ISBN
c Koichi Suga, 4 4 6 5 ISBN 978-4-64-6445- 4 ( ) x(t) t u(t) t {u(t)} {x(t)} () T, (), (3), (4) max J = {u(t)} V (x, u)dt ẋ = f(x, u) x() = x x(t ) = x T (), x, u, t ẋ x t u u ẋ = f(x, u) x(t ) = x T x(t
08-Note2-web
r(t) t r(t) O v(t) = dr(t) dt a(t) = dv(t) dt = d2 r(t) dt 2 r(t), v(t), a(t) t dr(t) dt r(t) =(x(t),y(t),z(t)) = d 2 r(t) dt 2 = ( dx(t) dt ( d 2 x(t) dt 2, dy(t), dz(t) dt dt ), d2 y(t) dt 2, d2 z(t)
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168 13 Maxwell ( H ds = C S rot H = j + D j + D ) ds (13.5) (13.6) Maxwell Ampère-Maxwell (3) Gauss S B 0 B ds = 0 (13.7) S div B = 0 (13.8) (4) Farad
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II A A441 : October 02, 2014 Version : Kawahira, Tomoki TA (Kondo, Hirotaka )
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338 7 7.3 LCR 2.4.3 e ix LC AM 7.3.1 7.3.1.1 m k x m x x > 0 x < 0 F x > 0 x < 0 F = k x k > 0 k 5.3.1.1 x = xt 7.3 339 m 2 x t 2 = k x 2 x t 2 = ω 2 0 x ω0 = k m ω 0 1.4.4.3 2 +α 14.9.3.1 5.3.2.1 2 x
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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
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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