Ψ (x, t) =
�
−iEt/ Asin 4πx a e 0 x<
a/2 ≤ x ≤ a/2 a/2 − a/2
a/2 ou x > a/2 a/2 −a/2 a/2 ≤ x ≤ a/2 a/2 −a/2
Ψ (x, t)
A
E = =
2
m a2
1, 0 n = 3 x=0
2
8π
A =
� 2
a
× 10−
9
x=L
L = 300 x = 0, 5 L
x = 0, 75 L
≥ −a (x) ψn (−x) = −ψn (x x
−a < x < a ψn (−x) = ψ n (x (x)
m
2
2
� ( � 2
a sin
2
2
a cos
nπ a x
≤ −a 2
0 < x < a x = x + x + a
� ( �
x
2
n
nπ a x
n
m Ψ (x, t) = Ae A e−a[(m x A
a σx A =
σ p =
2am
( �
√ am σ σ = x p
π
1 4
/)+it]
,
Ψ (x, t) Ψ (x, t)
V (x) 2 x x p p2 σ p 2
2
2
V (x) = 2ma x
x = 0
2
2
x =
4am
p = 0
2
p = am
ψ (x) = A e− E = = 2 /2mL2
L x
σx =
x2 2L2
�
4am
x x = L V (x) = m w2 x2 /2 V (x) ψ (x)
σx =
E = w/2
x
2
x2 2m L4
V (x) = x
w
K =
x2 σ p = p2
√ − √ − � − 2
x
x
2
p
2
2mL2
�− � x2 L2
1
x2
x 2
ψ
σx σ p
σx σ p
σ p =
h 2L
σx σ p =
1
+
2π 2
σx =
1 h 12 2
ˆ ∞ +
E cin. =
ψ ∗ (x)
−∞
�−
2
� −
L2 2π 2
+
L2 12
d2 ψ (x) dx 2m dx2
�
E
� �
i px
+ C − e−i
ψE (x, t) = C + e C ±
jE =
−i m 2
(
d ψE dx ψE
−
ω
�
ρE ∂ρ E ∂t
d ψE dx ψE
E =
px
p2 2m
∆x ∆ p =
e−i
Et
,
= ψE 2 E + ∂j ∂x = 0
| |
+ 12 mω2 x2
m
∆x ∆ p
2
h2 1 E = + mω2 x2 ; 2 2 32π m x 2
1 2
ω (∆x)2 = x2
E
Ψ (x, t) = ψ (x) e−iEt/
p = 0 H = ∆ p
p2 2m
+ 12 mω2 x2
∆x
x = 0 2
2
V (x) 2
p
2
p n
=1
=
h2 4L2
p = 2mE n=1 p n = Lh 2
2
=2
2
p = 2m [E − V (x)] n=2
x
σx =
x2 σ p = p2
√ − √ − � − 2
x
x
2
p
x2
x 2
ψ
σx σ p
σx σ p
σ p =
h
2L
σx σ p =
1 2π 2
+
σx =
1 h 12 2
� −
L2
2π 2
+
L2 12
t = 0
Ψ (x, 0) =
Ψ (x, 0)
A xa
se 0
x A bb− −a se
0
≤x≤a a< x ≤ b
se x < 0 ou x > b, A
a
b
Ψ (x, 0) a x
V (x) = V 0 E = V 0 /2 x>
A =
�
0
se x
V 0
se x > 0 (
3
b
a b
2a+b 4
≤0 (
) ),
x < 0 R x > 0
E = 2V 0
R
ψII (x)
∝ e−
√
mV 0
T R = 1 √ (2− 2) √ R = (2+ 2)
2
x
2
x > 0
√ T = 8 √ 2 2+ 2 (
)
2
V = 0 x>0 k1
R + T = 1
E = 2V 0
x<0
V =
−V
0
T = 5, 88
× 10−
8
T = 1, 25
× 10−
3
T = 4, 2 10−5
5, 6V
×
V 0 > E
E
� √ √ � 1
2 5
1+
2 5
−
1
� √ � − √ 1
2 5
1+
2 5
−
2
V = 0 V =
x
∞
ψn1,n2 (x, y) =
2
L
sin
n1 π L x
n2 π L y
( � ( � sin
0 < x < L 0 < y < L
y
2
E n1,n2 =
π2
2mL2
(
n21 + n22
�
(n1 , n2 )
≡ {(1, 2) , (2, 1)}
∆r = 0.02a0 ∆r = 0.02a0 0, 0107
a0
2
r = a 0
r = 2a0 0, 0059 r = 32 a0
ψnlml (r,θ,ϕ) = Rnl (r) Y lml (θ, ϕ)
E n E 2 n = 2
R21 (r) =
1
r − e 2 6a a0
√
3 0
pnl = R 2nl r2
r 2a0
,
n = 2 4a0
