mécanique quantique (7) et physique statistique (11)

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Le cours de physique (18 blocs) :

mécanique quantique (7) et physique statistique (11)

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Outils pour le cours de mécanique quantique

Livres (existent aussi en anglais) :

•! « Mécanique quantique »

•! « Problèmes quantiques » Jean-Louis Basdevant et Jean Dalibard

Chaque semaine: un QCM à remplir à l’adresse :

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Idées clés de la description quantique d'un système physique :

Principes de la mécanique quantique

!! Etats du système

!! "Observables" de ce système

!! Evolution dans le temps du système

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B ˆ (5)

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[ ˆ A, B] ˆ ≡ A ˆ B ˆ − B ˆ A ˆ (7)

[ ˆ A, B] = 0 ˆ (8)

| ψ

i

" (9)

α

_i

β

_i

(10)

ˆ p

_x

= ¯ h

i

∂

∂x (11)

ψ(x, y, z) = e

^ik^x^x

φ(y, z ) (12)

‘

¯

hk

x

(13)

ˆ p

y

= ¯ h

i

∂

∂y (14)

ψ(x, y, z) = e

^ik^y^y

χ(x, z) (15)

R$.4(&+#1'7%'(!'.!)"+-4(%'(%'(#12'7%'(J!/%'

y

':''

W%&'#.0)!"%4)&'''''''%"''''''''-#$$4"%1"='e1'.%4"'.)0.!)%)'(!'.!)"+-4(%'7!1&' 41'0"!"'#t'(J+$.4(&+#1'&%(#1':'%"'(J+$.4(&+#1'&%(#1'F'&#1"'&+$4("!10$%1"''

@+%1'70>+1+%&':'

! ψ | A ˆ

²

| ψ " = a

²_α

(1)

! ψ | A ˆ | ψ " = a

α

(2)

| ψ " (3)

A ˆ (4)

B ˆ (5)

A ˆ B ˆ = ˆ B A ˆ (6)

[ ˆ A, B] ˆ ≡ A ˆ B ˆ − B ˆ A ˆ (7)

[ ˆ A, B] = 0 ˆ (8)

| ψ

i

" (9)

α

_i

β

_i

(10)

ˆ p

_x

= ¯ h

i

∂

∂x (11)

ψ(x, y, z) = e

^ik^x^x

φ(y, z) (12)

‘

¯

hk

x

(13)

ˆ p

y

= ¯ h

i

∂

∂y (14)

ψ(x, y, z) = e

^ik^y^y

χ(x, z) (15)

ψ(x, y, z) = e

^ik^x^x

e

^ik^y^y

F (z) (16)

! ψ | A ˆ

²

| ψ " = a

²_α

(1)

! ψ | A ˆ | ψ " = a

_α

(2)

| ψ " (3)

A ˆ (4)

B ˆ (5)

A ˆ B ˆ = ˆ B A ˆ (6)

[ ˆ A, B] ˆ ≡ A ˆ B ˆ − B ˆ A ˆ (7)

[ ˆ A, B] = 0 ˆ (8)

| ψ

_i

" (9)

α

i

β

i

(10)

ˆ p

x

= ¯ h

i

∂

∂x (11)

ψ(x, y, z) = e

^ik^x^x

φ(y, z) (12)

‘

¯

hk

x

(13)

ˆ p

_y

= ¯ h

i

∂

∂y (14)

ψ(x, y, z) = e

^ik^y^y

χ(x, z) (15)

ψ(x, y, z) = e

^ik^x^x

e

^ik^y^y

F (z) (16)

! ψ | A ˆ

²

| ψ " = a

²_α

(1)

! ψ | A ˆ | ψ " = a

_α

(2)

| ψ " (3)

A ˆ (4)

B ˆ (5)

A ˆ B ˆ = ˆ B A ˆ (6)

[ ˆ A, B] ˆ ≡ A ˆ B ˆ − B ˆ A ˆ (7)

[ ˆ A, B] = 0 ˆ (8)

| ψ

_i

" (9)

α

i

β

i

(10)

ˆ p

x

= ¯ h

i

∂

∂x (11)

ψ(x, y, z) = e

^ik^x^x

φ(y, z) (12)

‘

¯

hk

x

(13)

ˆ p

_y

= ¯ h

i

∂

∂y (14)

ψ(x, y, z) = e

^ik^y^y

χ(x, z) (15)

ψ(x, y, z) = e

^ik^x^x

e

^ik^y^y

F (z) (16)

MM:N'

:%

c/%$.(%'F:'-#$$%1"'"+)%)'.!)"+'7J41%'&6$0")+%'r'

*#4K%$%1"'7!1&'41'.#"%1"+%('.!+)'

!K%-'

e1'+1")#74+"'(J#.0)!"%4)'8.!)+"09''''''70>+1+'.!)' W!'&6$0")+%'7%'(J5!$+("#1+%1'&%'")!74+"'.!)':'

[!(%4)&'.)#.)%&':'

c"!"&'.)#.)%&:'>#1-"+#1&'.!+)%&'#4'+$.!+)%&' e1'.%4"'-5%)-5%)'(%&'0"!"&'.)#.)%&'7%'''''''

&#4&'>#)$%'7%'>#1-"+#1&'.!+)%&'#4'+$.!+)%&'

%"'''''''#1"'7#1-'41%'@!&%'7%'>#1-"+#1&'.)#.)%&'-#$$41%&'

H

ˆ (1)

Etot.

= ¯

h²K²

2M +

Erel.

(2)

−

¯

h²

2µ

∆ψ("r

) +

V

("

r

)ψ("

r

) =

Erel.

ψ("

r

) (3)

H

ˆ

rel.

ψ =

Erel.

ψ (4)

Ψ(R,

" "

r

) =

eⁱ^K^!^·^R^!

ψ("

r

) (5)

¯

h²K²

2M (6)

eiK

"

·R

" (7)

Φ("re,

"

rp

) = ψ(

R,

" "

r

) (8)

[ ˆ

Hc.m.,H

ˆ

rel.

] = 0 (9)

[ˆ

x,p

ˆ

x

] =

i¯h

(10)

[ ˆ

X,P

ˆ

x

] =

i¯h

(11)

" ˆ

R, P

" ˆ (12)

" ˆ

r,

"

p

ˆ (13)

µ

=

mpme

mp

+

me

(14)

H

ˆ

rel.

=

p

ˆ

²

2µ +

V

(ˆ "

r)

(15)

M

=

mp

+

me

(16)

H

ˆ

c.m.

=

P

ˆ

²

2M (17)

H

ˆ = ˆ

Hc.m.

+ ˆ

Hrel.

(18)

P

ˆ (1)

H

ˆ (2)

Etot.

= ¯

h²K²

2M +

Erel.

(3)

−

¯

h²

2µ

∆ψ("r

) +

V

("

r

)ψ("

r

) =

Erel.

ψ("

r

) (4)

H

ˆ

rel.

ψ =

Erel.

ψ (5)

Ψ(R,

" "

r

) =

eⁱ^K·^! ^R^!

ψ("

r

) (6)

¯

h²K²

2M (7)

eiK

"

·R

" (8)

Φ("re,

"

rp

) = ψ(

R,

" "

r

) (9)

[ ˆ

Hc.m.,H

ˆ

rel.

] = 0 (10)

[ˆ

x,p

ˆ

x

] =

i¯h

(11)

[ ˆ

X,P

ˆ

x

] =

i¯h

(12)

" ˆ

R, P

" ˆ (13)

" ˆ

r,

"

p

ˆ (14)

µ

=

mpme

mp

+

me

(15)

H

ˆ

rel.

=

p

ˆ

²

2µ +

V

(ˆ "

r)

(16)

M

=

mp

+

me

(17)

H

ˆ

c.m.

=

P

ˆ

²

2M (18)

H

ˆ = ˆ

Hc.m.

+ ˆ

Hrel.

(19)

(7)

! ψ | A ˆ

²

| ψ " = a

²_α

(1)

! ψ | A ˆ | ψ " = a

_α

(2)

| ψ " (3)

A ˆ (4)

B ˆ (5)

A ˆ B ˆ = ˆ B A ˆ (6)

[ ˆ A, B] ˆ ≡ A ˆ B ˆ − B ˆ A ˆ (7)

[ ˆ A, B] = 0 ˆ (8)

[ ˆ A, B] ˆ % = 0 (9)

| ψ

_i

" (10)

α

_i

β

_i

(11)

ˆ p

_x

= ¯ h

i

∂

∂x (12)

ψ(x, y, z) = e

^ik^x^x

φ(y, z) (13)

‘

¯

hk

x

(14)

ˆ p

_y

= ¯ h

i

∂

∂y (15)

ψ(x, y, z) = e

^ik^y^y

χ(x, z) (16)

ψ(x, y, z) = e

^ik^x^x

e

^ik^y^y

F (z) (17)

ˆ

p

x

(18)

e@&%)K!@(%&'34+'1%'-#$$4"%1"'.!&'

P+'7%4/'#@&%)K!@(%&'1%'-#$$4"%1"'.!&Z'-J%&"aXa7+)%'&+'''''''''''''''''''''''Z' +('1J%&"'%1'2010)!('.!&'.#&&+@(%'7%'.)0.!)%)'(%'&6&",$%'7!1&'41'0"!"'#t'' (%&'34!1"+"0&'

A

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'&#1"'@+%1'70"%)$+10%&=''

A(4&'.)0-+&0$%1"':'

! ψ | A ˆ

²

| ψ " = a

²_α

(1)

! ψ | A ˆ | ψ " = a

_α

(2)

| ψ " (3)

A ˆ (4)

B ˆ (5)

A ˆ B ˆ = ˆ B A ˆ (6)

[ ˆ A, B] ˆ ≡ A ˆ B ˆ − B ˆ A ˆ (7)

[ ˆ A, B] = 0 ˆ (8)

[ ˆ A, B] ˆ % = 0 (9)

| ψ

i

" (10)

α

_i

β

_i

(11)

ˆ p

x

= ¯ h

i

∂

∂x (12)

ψ(x, y, z) = e

^ik^x^x

φ(y, z) (13)

‘

¯

hk

x

(14)

ˆ p

y

= ¯ h

i

∂

∂y (15)

ψ(x, y, z) = e

^ik^y^y

χ(x, z) (16)

ψ(x, y, z) = e

^ik^x^x

e

^ik^y^y

F (z) (17)

ˆ

p

x

(18)

∆a ∆b ≥ 1 2

! !

!! ψ | [ ˆ A, B] ˆ | ψ " ! ! !

->='AI'

(19)

c/%$.(%':'(%'-#4.(%'.#&+"+#1'+$.4(&+#1'&%(#1'41'$H$%'!/%='

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(9)

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!(#)&' n=1

n=2

n=0

∆a∆b≥ 1 2

!!

!"ψ|[ ˆA,B]ˆ|ψ#!!! (19)

ψ0(x)∝e⁻^x²^/2a² (20)

∆a∆b≥ 1 2

!!

!"ψ|[ ˆA,B]ˆ|ψ#!

!! (19)

ψ0(x)∝e^−x²^/2a² (20)

ψ1(x)∝x e^−x²^/2a² (21)

∆a ∆b ≥ 1 2

! !

!" ψ | [ ˆ A, B] ˆ | ψ # ! ! ! (19)

ψ

₀

(x) ∝ e

⁻^x²^/2a²

(20)

ψ

₁

(x) ∝ x e

⁻^x²^/2a²

(21)

a = "

¯

h/mω (22)

(E

1

− E

0

)/¯ h = ω (23)

" x # (t) = a

√ 2 cos(ωt) (24)

ω (25)

∆a∆b≥ 1 2

!!

!"ψ|[ ˆA,B]ˆ|ψ#!

!! (19)

ψ0(x)∝e⁻^x²^/2a² (20)

ψ1(x)∝x e^−x²^/2a² (21)

a="

¯

h/mω (22)

(E1−E0)/¯h=ω (23)

"x#(t) = a

√2 cos(ωt) (24)

ω (25)

Aˆ (26)

¯

hω (27)

!(#)&'

*#74(!"+#1'7%''''''''''''''''''''X'(!'.4(&!"+#1'

∆a∆b≥ 1 2

!!

!"ψ|[ ˆA,B]ˆ|ψ#!

!! (19)

ψ

0(x)∝e^−x²^/2a² (20)

ψ

1(x)∝x e^−x²^/2a² (21)

a="

¯

h/mω (22)

(E1−E0)/¯h=

ω

(23)

A!)'%/%$.(%':' P+'(V0"!"'+1+"+!('%&"'

!x"(t) =x₀ cos(ωt) (1)

!ψ|Aˆ²|ψ"=a²_α (2)

!ψ|Aˆ|ψ"=a_α (3)

|ψ" (4)

Aˆ (5)

Bˆ (6)

AˆBˆ = ˆBAˆ (7)

[ ˆA,B]ˆ ≡ AˆBˆ−BˆAˆ (8)

[ ˆA,B] = 0ˆ (9)

[ ˆA,B]ˆ %= 0 (10)

|ψ_i" (11)

αi βi (12)

ˆ p_x= ¯h

i

∂

∂x (13)

ψ(x, y, z) =e^ik^x^xφ(y, z) (14)

‘

¯

hkx (15)

ˆ p_y= ¯h

i

∂

∂y (16)

ψ(x, y, z) =e^ik^y^yχ(x, z) (17)

ψ(x, y, z) =e^ik^x^xe^ik^y^yF(z) (18)

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