Lecture 18:
02/27/09
4.5
4
3.5
E/ h ω
3
2.5
2
1.5
1
0.5
0
-5
V(x)
En
ψ (x)
0
x
5
II2,3 Qualitative Plots of Bound-State Wave Functions:
n=3
:
II2,4 Square Well of Finite Depth, part II :
10
8
6
4
2
0
-2
-4
-6
tan(θ
θ)
(θ
θ02/ θ 2-1)1/2 for V0 =1eV
-8
(θ
θ20 /θ
θ2 -1)1/2 for V0=10eV
-10
0
(θ
θ20 /θ
θ2 -1)1/2 for V0=100eV
pi/2
pi
3pi/2 2pi
θ = kL/2
5pi/2
3pi
7pi/2
10
8
cot(θ)
-(θ02/ θ2-1)1/2 for V0=1eV
6
-(θ02/θ2-1)1/2 for V0=10eV
4
-(θ02/θ2-1)1/2 for V0=100eV
2
0
-2
-4
-6
-8
-10
0
pi/2
pi
3pi/2 2pi
θ = kL/2
5pi/2
3pi
7pi/2
10
10
8
8
6
6
4
4
2
2
0
0
En
ψ (x)
V(x)
-2
-1
-0.5
En
ψ (x)
V(x)
0
x/L
0.5
1
-2
-1
-0.5
0
x/L
0.5
1
II2,5 The simple harmonic oscillator potential V(x)=1/2cx2: