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)



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, y, z) (15)

x = x cos0 + y sin0 (16)

y = x sin0 + y cos0 (17)

z = z (18)

2Q#

X&B/1)/&("#0/1#1%'/')%"'#$%$"&'#()&*')+,"#

!>)&B/1)/&("#0/1#1%'/')%

X&B/1)/&("#0/1#1%'/')%H#1Y6"#*+,)B/6"&'#0%,1#'%,'";#6";#5)1"(')%&;#5"#6>";0/("#

$%&'()*+,-*.&/01()H#

Z/'.*$/')+,"$"&'I#%*(1)'#("''"#)&B/1)/&("#")&'1%5,);/&'##

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)



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)



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, y, z) (10)


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)



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, y, z) (10)


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)

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Z%$"&'#()&*')+,"#2 :

m

0

1

-1

1

2

-2

2 tats p

(EQ#%1,&"#$%6*(,6"#H#

h)

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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V,#;")"#("#@/\#5>/'%$";I#5";#$%6*(,6";#

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Cours Momentcinétique