O x, y, z, t, O2 x2 , y2 , z2 , t2
4
v = c x = x2
5
y y2 z z2
t = t2 = 0
R
6
3
u = c T
5




i - - -
i j j k k
z1 z2 z3 z4 z5 z6
�
zi i " 6 = 1, 2, 3, 4, 5, 6 i
yi i
p1 : EA T p2 : EA V
�
zi yi i " 6
R
T



"z ,yi, 1 d" i d" j d" 6
i

EG
(EG, T, V, Ą) Ą : EG T � : T EG
Ą ć% � = idT

�1(t) = (t, xo), t " T
�2(t) = (t, xo + vot), t " T

1
�3(t) = (t, xo + vot + gt2), t " T
2
�4(t) = (t, xo cos(�t)), t " T
V = R


mć = F

F = -kx
x(t) = x0 + vt
x(t) = x0 + vt + vt2/2m
x(t) = x0 cos(�t + �)


�
t = 0

l1 m1
l2 m2

Q
Q = {(ą1, ą2)|0 d" ą1 < 2Ą, 0 d" ą2 <
2Ą} 2Ą





(a) V = const, (b) V = (F/m)x, (c) V = kx2/2.
T V
E


V (x, y, z) = -mgz
"
V (x, y, z) = C/ x2 + y2 + z2
V (x, y, z) =
(1/2)k(x2 + y2 + z2).

(0, 0)
l1 l2 m1 m2
(ą1, ą2) 0 d" ą1 < 2Ą 0 d" ą2 < 2Ą

Q
(ą1, ą2)



1 1
2 2
T = l1ą12 + m2l2ą22 + m1l1l2ą1ąŁ cos(ą1 - ą2)
Ł Ł Ł
2
m1 + m2 2

V = -gl1(m1 + m2) cos(ą1) - gm2l2 cos(ą2)






x + �2x = 0 x(t) = Acos(�t + �)
A �
x(0) = 0 �(0) = v0
x(0) = x0 �(0) = 0


V (x, y, z) = mgz

C
V (r, Ń, �) =
r

V (r, Ń, �) = kr2



= a( + j + k)
r i







�ł �ł �ł �ł
5 2 0 2 7 1 3 1
�ł �ł �ł �ł
�ł �ł �ł �ł
2 5 2 0 1 7 1 3
�ł �ł �ł �ł
V1 = V2 =
�ł �ł �ł �ł
�ł �ł �ł �ł
0 2 5 2 3 1 7 1
�ł łł �ł łł
2 0 2 5 1 3 1 7
specV1 = (1, 5, 5, 9) specV2 = (4, 4, 8, 12)

 = 5 V1  = 4 V2
q = a(e1 - e3) + b(e2 - e4) a, b
e1, e2, e3, e4









a, b


1 1 1
" " |0,
|Ć >= |2, 1, 0 > + | - 1, 0, 2 > -" -2, -1 >
3 2 6


 px py pz p2 =
Ć Ć Ć
px + py + pz
Ć Ć Ć

n n = 0, 1, 2, 3 . . .
x, y, z
Oh
g " Oh

A, B, C, D, A2 , B2 , C,2 D,2

Oh
Oh
A
Oh = D2h C3V
D2h
A
|pqr > C3V



|nxnynz >
Oh

l

p2 + q2 + r2 = l





(L)2 Lz


j1 = 1 j2 = 1
j1 = 1/2 j2 = 2
j1 = 1 j2 = 2
J
LS
(1s)1 (2p)1 (2p)2 (3d)1 (3d)2 (3d)8 (3d)9
4
I

(l1, l2) (1, 1) (1, 2) (2, 2) (1/2, 1/2)
(1/2, 2)
|l1m1 > |l2m2 >

|l1l2LM >



n
4s 4p 4d 4f

1s2, 2p2, 2p3, 2p4, 3d2, 3d3, 3d5, 3d9, 3d10, 4f2, 4f3, 4f7, 4f12.

 3d3