4. Quantum mechanics I Fall 2012
Physics 451
Quantum mechanics I
Fall 2012
Oct 1, 2012
Karine Chesnel

5. HW # 9 due Tuesday Oct 4 by 7pm Pb 2.27, 2.29, 2.30, 2.31
Quantum mechanics
Announcements
Homework this week:
HW # 9 due Tuesday Oct 4 by 7pm
Pb 2.27, 2.29, 2.30, 2.31
HW # 10 due Thursday Oct 7 by 7pm

6. The delta function potential
Ch 2.5
Quantum mechanics
The delta function potential
For
Continuity at boundaries
is continuous
is continuous except where V is infinite

7. The delta function well
Ch 2.5
Quantum mechanics
The delta function well
Bound state
Pb 2.27 double delta well
2 boundaries, 4 conditions

8. The delta function well
Ch 2.5
Quantum mechanics
The delta function well
Scattering state x
Travelling waves A B F G
Continuity at boundary
(A,B, F,G) ?

9. The delta function well
Ch 2.5
Quantum mechanics
The delta function well
Scattering state A F B x
Travelling waves
Reflected wave
Transmitted wave

10. The delta function well
Ch 2.5
Quantum mechanics
The delta function well
Scattering state A F B x
Reflection coefficient
Transmission coefficient

11. The delta function potential
Ch 2.5
Quantum mechanics
The delta function potential
Scattering state

12. The delta function barrier
Ch 2.5
Quantum mechanics
The delta function barrier
Scattering state only A F B x
“Tunneling”
Reflection coefficient
Transmission coefficient

13. Quiz 13 Quantum mechanics
A particle can tunnel trough an infinite barrier
with some relatively small thickness
Yes No

14. The finite square well Quantum mechanics V(x) Scattering states -a a x
Bound states
-V0

15. The finite square well Quantum mechanics V(x) x -V0 Ch 2.6
Continuity at boundaries
V(x) x
-V0
is continuous
X=+a
X=-a

16. Ch 2.6
Quantum mechanics
The finite square well
Bound state
For
For

17. The finite square well Quantum mechanics Ch 2.6 Bound state For
General solution

18. The finite square well Quantum mechanics x -V0 Pb 2.30 normalization
Symmetry considerations
V(x)
The potential is even function about x=0
The solutions are either even or odd! x
-V0
Pb 2.30 normalization

19. The finite square well Quantum mechanics x -V0
Continuity at boundaries
V(x) x
-V0
Continuity of

20. Quantum mechanics
The finite square well
Bound states
where

21. The finite square well Quantum mechanics V(x) V(x) x x -V0 -V0
Bound states
V(x) x
-V0
Wide, deep well
large
(large a or V0)
Shallow, narrow well
V(x) x
-V0
small
(small a, V0)
One bound state
Pb 2.29 odd solution
Pb 2.31 extrapolation to infinite delta well