1. Quantum mechanics II Winter 2012
Physics 452
Quantum mechanics II
Winter 2012
Karine Chesnel

2. Tuesday Feb 1: Homework # 7
Phys 452
Homework
Tuesday Feb 1: Homework # 7
Pb 6.23, 6.24, 6.25, 6.27, 6.28
Review 1: M –W classes
Test 1: Thu- Sat, testing center

3. The fine structure of hydrogen
Phys 452
The fine structure of hydrogen
Fine structure
Bohr’s
energy
Relativistic
correction +
Spin-orbit
coupling +
E =

4. The fine structure of hydrogen
Phys 452
The fine structure of hydrogen
Bohr’s
energy
E =
+ Fine structure
+ Zeeman effect ?
Pb 6.17
New relevant quantum numbers:
n, l, s, j and mj

5. Zeeman effect Phys 452 Effect of an external field Bext S L e-
“Classical view” e- S L
Bext

6. Zeeman effect Phys 452 Bext S L Comparing: and e- Pb 6.20 Intermediate
“Classical view” e- S L
Bext
Comparing: and
Pb 6.20
Weak-field
Strong field
Intermediate
field
Fine structure
dominates
Zeeman effect
dominates

7. Quiz 9a Phys 452 What is the best set of quantum numbers
to express the weak-field Zeeman effect ? C. D. E.

8. Zeeman effect Phys 452 Bext S Weak -field L Good eigenstates: e-
with Lande factor:
Pb 6.21

9. Quiz 9b Phys 452 What is the best set of quantum numbers
to express the strong-field Zeeman effect ? C. D. E.

10. Zeeman effect Phys 452 Bext S Strong -field L Good eigenstates: e-
Pb 6.23,6.24

11. Zeeman effect Phys 452 Bext S intermediate -field L e- Clebsch-Gordan
Pb 6.25

12. Hyperfine splitting Phys 452 Sp Se Bp electron: e- , me Proton: e+, mp
“Spin – spin” interaction
Magnetic interaction between the spin of the electron and
the magnetic field produced by the spin of the proton at a distance

13. Phys 452
Hyperfine splitting Sp Se Bp
electron: e- , me
Proton: e+, mp

14. Hyperfine splitting Phys 452 Sp Se Bp Pb 6.27 electron: e- , me
Proton: e+, mp
1/pa3
for =0
when l=0
Pb 6.27

15. Hyperfine splitting Phys 452 Sp Se Bp Pb 6.28 electron: e- , me
Proton: e+, mp
Two-particles system:
Triplet
Singulet
Pb 6.28
Application to
various types
of particles

16. Hyperfine splitting Phys 452 E First observed in 1881 by Michelson
Microwave
- radiowave
Explained in 1924 by Pauli
Radiation
omnipresent
in the interstellar
medium