1. Quantum mechanics I Fall 2012
Physics 451
Quantum mechanics I
Fall 2012
Sep 28, 2012
Karine Chesnel

2. Homework this week: HW # 8 due Friday Sep 28 by 5pm
Quantum mechanics
Announcements
Homework this week: HW # 8
due Friday Sep 28 by 5pm
Homework next week:
HW # 9 due Tuesday Oct 2 by 7pm
HW # 10 due Thursday Oct 4 by 7pm

3. Bound and Scattering states
Ch 2.5
Quantum mechanics
Bound and Scattering states
V(x) x
In physical reality:
Scattering state
Bound state

4. The Dirac delta function
Ch 2.5
Quantum mechanics
The Dirac delta function
for
for

5. The delta function potential
Ch 2.5
Quantum mechanics
The delta function potential
For

6. The delta function potential
Ch 2.5
Quantum mechanics
The delta function potential
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
For

8. The delta function well
Ch 2.5
Quantum mechanics
The delta function well
Bound state

9. Quiz 12a None One Two An infinity Quantum mechanics
How many bound states can be found
for a given delta function well potential?
None
One
Two
An infinity

10. The delta function well
Ch 2.5
Quantum mechanics
The delta function well
Scattering state

11. Quiz 12b None One Two An infinity Quantum mechanics
How many scattering states can be found
for a given delta function well potential?
None
One
Two
An infinity

12. 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) ?

13. 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

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

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

16. 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