Cours Momentcinétique
description
Transcript of Cours Momentcinétique
-
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!L = !r !p (1)
!p =h
i! (2)
H(r,) = (r,) H(r,+ 0) = (r,+ 0) (3)
R(0)(r,) = (r,+ 0) (4)
HR = RH (5)
0 (6)
(x, y, z) (7)
(x cos0 + y sin0 , x sin0 + y cos0 , z) (8)
[Rz(0)](x, y, z) = (x cos0 + y sin0 , x sin0 + y cos0 , z) (9)
0 0 $ 1 (10)
[Rz(0)](x, y, z) % (x, y, z) + 0(y
x x
y
)(11)
Rz(0) % 1 i0h
Lz (12)
Lx, Ly, Lz (13)
[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (14)
{H, Lx} {H, Ly} {H, Lz} (15)
{H, Lx, Ly, Lz} (16)
(17)
!L = !r !p (1)
!p =h
i! (2)
(x, y, z) (3)
H(r,) = (r,) H(r,+ 0) = (r,+ 0) (4)
R(0)(r,) = (r,+ 0) (5)
HR = RH (6)
0 (7)
(x, y, z) (8)
(x cos0 + y sin0 , x sin0 + y cos0 , z) (9)
[Rz(0)](x, y, z) = (x cos0 + y sin0 , x sin0 + y cos0 , z) (10)
0 0 $ 1 (11)
[Rz(0)](x, y, z) % (x, y, z) + 0(y
x x
y
)(12)
Rz(0) % 1 i0h
Lz (13)
Lx, Ly, Lz (14)
[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (15)
{H, Lx} {H, Ly} {H, Lz} (16)
{H, Lx, Ly, Lz} (17)
(18)
"'#5"#$W$"#0%,1##Lx, Ly (1)
0 ! 1 (2)
[Rz(0)](x, y, z) " (x+ 0y , 0x+ y , z) (3)
y " 0x + y (4)
x " x + 0y (5)
#L = #r #p (6)
#p =h
i# (7)
(x, y, z) (8)
H(r,) = (r,) H(r,+ 0) = (r,+ 0) (9)
R(0)(r,) = (r,+ 0) (10)
HR = RH (11)
0 (12)
(x, y, z) (13)
(x cos0 + y sin0 , x sin0 + y cos0 , z) (14)
(x, y, z) (15)
x = x cos0 + y sin0 (16)
y = x sin0 + y cos0 (17)
z = z (18)
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6>%0*1/'",1#1%'/')%##########5>,/&@6"#####/,'%,1#5>,/A"######5%&&*#H(r,) = (r,) H(r,+ 0) = (r,+ 0) (1)
R(0)(r,) = (r,+ 0) (2)
HR = RH (3)#####";'#)&B/1)/&'#0/1#1%'/')%)#
H(r,) = (r,) H(r,+ 0) = (r,+ 0) (1)
R(0)(r,) = (r,+ 0) (2)
HR = RH (3)
[A"$06"#H#1%'/')%/,'%,1#5"#6>/A"#z#8(%%15%&&*";#0%6/)1";#C#NO9#
!L = !r !p (1)
!p =h
i! (2)
(x, y, z) (3)
H(r,) = (r,) H(r,+ 0) = (r,+ 0) (4)
R(0)(r,) = (r,+ 0) (5)
HR = RH (6)
0 (7)
(x, y, z) (8)
(x cos0 + y sin0 , x sin0 + y cos0 , z) (9)
[Rz(0)](x, y, z) = (x cos0 + y sin0 , x sin0 + y cos0 , z) (10)
0 0 $ 1 (11)
[Rz(0)](x, y, z) % (x, y, z) + 0(y
x x
y
)(12)
Rz(0) % 1 i0h
Lz (13)
Lx, Ly, Lz (14)
[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (15)
{H, Lx} {H, Ly} {H, Lz} (16)
{H, Lx, Ly, Lz} (17)
(18)
V (r) = q2
4pi"0r
x
y
tournee(r,) = [Rz,] (r,) = (r, )
R!u, !u
G0*1/'",1#1%'/')%/,'%,1#5"#G\#8(%%15%&&*";#(/1'*;)"&&";9#
:%'/')%>,/&@6"#####/,'%,1#5"#6>/A"#G\#H#
y
x
H(r,) = (r,) H(r,+ 0) = (r,+ 0) (1)
R(0)(r,) = (r,+ 0) (2)
HR = RH (3)
0 (4)
(x, y, z) (5)
(x cos0 + y sin0 , x sin0 + y cos0 , z) (6)
[Rz(0)](x, y, z) = (x cos0 + y sin0 , x sin0 + y cos0 , z) (7)
0 0 " 1 (8)
[Rz(0)](x, y, z) # (x, y, z) + 0(y
x x
y
)(9)
Rz(0) # 1 i0h
Lz (10)
Lx, Ly, Lz (11)
!L = !r !p (1)
!p =h
i! (2)
(x, y, z) (3)
H(r,) = (r,) H(r,+ 0) = (r,+ 0) (4)
R(0)(r,) = (r,+ 0) (5)
HR = RH (6)
0 (7)
(x, y, z) (8)
(x cos0 + y sin0 , x sin0 + y cos0 , z) (9)
(x, y, z) (10)
[Rz(0)](x, y, z) = (x cos0 + y sin0 , x sin0 + y cos0 , z) (11)
0 0 $ 1 (12)
[Rz(0)](x, y, z) % (x, y, z) + 0(y
x x
y
)(13)
Rz(0) % 1 i0h
Lz (14)
Lx, Ly, Lz (15)
[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (16)
{H, Lx} {H, Ly} {H, Lz} (17)
{H, Lx, Ly, Lz} (18)
x = x cos + y siny = x sin + y cos
= (x cos+ y sin , x sin+ y cos , z)tournee(x, y, z) =
z = z
[Rz,] (x, y, z) = (x, y, z)
(>";']C]5)1"#H#
H#@*&*1/'",1;#)&E)&)'*;)$/,A#5,#@1%,0"#5";#1%'/')%&;#
H(r,) = (r,) H(r,+ 0) = (r,+ 0) (1)
R(0)(r,) = (r,+ 0) (2)
HR = RH (3)
0 (4)
(x, y) (5)
(x cos0 + y sin0 , x sin0 + y cos0) (6)
[Rz(0)](x, y) = (x cos0 + y sin0 , x sin0 + y cos0) (7)
0 0 " 1 (8)
[Rz(0)](x, y) # (x, y) + 0(y
x x
y
)(9)
Rz(0) # 1 i0h
Lz (10)
Lx, Ly, Lz (11)
:%'/')%)&E)&)'*;)$/6"#/,'%,1#5"#3\#H#
y
x
H(r,) = (r,) H(r,+ 0) = (r,+ 0) (1)
R(0)(r,) = (r,+ 0) (2)
HR = RH (3)
0 (4)
(x, y, z) (5)
(x cos0 + y sin0 , x sin0 + y cos0 , z) (6)
[Rz(0)](x, y, z) = (x cos0 + y sin0 , x sin0 + y cos0 , z) (7)
0 0 " 1 (8)
[Rz(0)](x, y, z) # (x, y, z) + 0(y
x x
y
)(9)
Rz(0) # 1 i0h
Lz (10)
Lx, Ly, Lz (11)
!L = !r !p (1)
!p =h
i! (2)
(x, y, z) (3)
H(r,) = (r,) H(r,+ 0) = (r,+ 0) (4)
R(0)(r,) = (r,+ 0) (5)
HR = RH (6)
0 (7)
(x, y, z) (8)
(x cos0 + y sin0 , x sin0 + y cos0 , z) (9)
(x, y, z) (10)
[Rz(0)](x, y, z) = (x cos0 + y sin0 , x sin0 + y cos0 , z) (11)
0 0 $ 1 (12)
[Rz(0)](x, y, z) % (x, y, z) + 0(y
x x
y
)(13)
Rz(0) % 1 i0h
Lz (14)
Lx, Ly, Lz (15)
[H, Lx] = 0 [H, Ly] = 0 [H, Lz] = 0 (16)
{H, Lx} {H, Ly} {H, Lz} (17)
{H, Lx, Ly, Lz} (18)
V#6>%151"#2#"#
x ! x + yy ! x + yz = z
! 1
[Rz,] (x, y, z) ! (x+ y , x+ y , z)
! (x, y, z) + (y
x x
y
)
Rz, ! 1 i! Lz
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LzY0,0(,) = 0 L+Y0,0(,) = 0 (1)
pi0
sin d 2pi0
d |Y",m(,)|2 = 1 (2)
H R(0) = R(0) H (3)
R(0) (4)
= R(0) (r,) = R(0)(H (r,)
)= H
(R(0)(r,)
)(5)
H (6)
(r,+ 0) = H(r,+ 0) (7)
(r,) = H(r,) (8)
H(r,) = (r,) H(r,+ 0) = (r,+ 0) (9)
(10)
Lx, Ly (11)
0 ! 1 (12)
[Rz(0)](x, y, z) " (x+ 0y , 0x+ y , z) (13)
y " 0x + y (14)
x " x + 0y (15)
%L = %r %p (16)
%p =h
i% (17)
(x, y, z) (18)
LzY0,0(,) = 0 L+Y0,0(,) = 0 (1)
pi0
sin d 2pi0
d |Y",m(,)|2 = 1 (2)
H R(0) = R(0) H (3)
R(0) (4)
= R(0) (r,) = R(0)(H (r,)
)= H
(R(0)(r,)
)(5)
H (6)
(r,+ 0) = H(r,+ 0) (7)
(r,) = H(r,) (8)
H(r,) = (r,) H(r,+ 0) = (r,+ 0) (9)
(10)
Lx, Ly (11)
0 ! 1 (12)
[Rz(0)](x, y, z) " (x+ 0y , 0x+ y , z) (13)
y " 0x + y (14)
x " x + 0y (15)
%L = %r %p (16)
%p =h
i% (17)
(x, y, z) (18)
!";#./1$%&)+,";#;0.*1)+,";#8;,)'"9#
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2 tats p
(EQ#%1,&"#$%6*(,6"#H#
h)
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d1 d2 M1 M2 (1)
I = M1d21 +M2d22 (2)
! = 0 ! = 1 ! = 2 (3)
LzY0,0(,) = 0 L+Y0,0(,) = 0 (4)
pi0
sin d 2pi0
d |Y",m(,)|2 = 1 (5)
H R(0) = R(0) H (6)
R(0) (7)
= R(0) (r,) = R(0)(H (r,)
)= H
(R(0)(r,)
)(8)
H (9)
(r,+ 0) = H(r,+ 0) (10)
(r,) = H(r,) (11)
H(r,) = (r,) H(r,+ 0) = (r,+ 0) (12)
(13)
Lx, Ly (14)
0 ! 1 (15)
[Rz(0)](x, y, z) " (x+ 0y , 0x+ y , z) (16)
y " 0x + y (17)
x " x + 0y (18)
`,"6#;0"('1"#0%,1#6"#$%,B"$"&'#5"#1%'/')%##
-6/;;)+,"$"&'I#6>*&"1@)"#5"#1%'/')%>*(1)'#H###
[Lx, Ly] = ihLz (19)
[Ly, Lz] = ihLx (20)
[Lz, Lx] = ihLy (21)
Lx =h
i
(y
z z
y
)(22)
Ly =h
i
(z
x x
z
)(23)
h 50 a` 500 meV (24)
E =L2
2I(25)
H#$%$"&'#5>)&"1')"#5"#6/#$%6*(,6"#
Z%6*(,6"#j#1%'/'",1#1)@)5"#
k/$)6'%&)"+,/&')+,"#H##
[Lx, Ly] = ihLz (19)
[Ly, Lz] = ihLx (20)
[Lz, Lx] = ihLy (21)
Lx =h
i
(y
z z
y
)(22)
Ly =h
i
(z
x x
z
)(23)
h 50 a` 500 meV (24)
E =L2
2I(25)
I =12MR2 (26)
H =L2
2I(27)
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