1. Quantum mechanics I Fall 2012
Physics 451
Quantum mechanics I
Fall 2012
Nov 16, 2012
Karine Chesnel

2. Homework this week: HW #20 Thursday Nov 17 by 10pm
Quantum mechanics
Announcements
Homework this week:
HW #20 Thursday Nov 17 by 10pm
Pb 4.27, 4.28, 4.29, 4.33, 4.34, 4.35
Practice Test 3 review
Mon Nov 19 – Tu Nov 20
Test 3 :
Monday Nov 26 – Friday Nov 30

3. Quantum mechanics
The Spin
Types of angular momentum
orbital
spin

4. Agular moment in the atom
Quantum mechanics
Agular moment in the atom
Orbital moment (l)
Spin moment (s)
Representation of

5. Spin in elementary particles
Quantum mechanics
Spin in elementary particles
Each elementary particle is characterized
by an immutable spin S
Fermions: (S half-integer)
Bosons: (S integer)
S=1/2
Leptons: electrons,…
Quarks: u,b,c,s,t,b
Proton, neutron
Photon
S=1
Mesons

6. Quantum mechanics
The spin

7. Quantum mechanics
The spin

8. Quantum mechanics
The spin 1/2
Spin up
Spin down
The “spinor”

9. Quantum mechanics
Pauli matrices
Pb 4.29

10. State of the electron Pb 4.27, 4.28, 4.29 Quantum mechanics
Normalization
Expectation values
etc…
Pb 4.27, 4.28, 4.29

11. When measuring Sx on an electron, what are the possible results?
Quantum mechanics
Quiz 29a
When measuring Sx on an electron, what are the possible results?
A. 0 B. D. E.

12. Quantum mechanics
Adding spins
Possibilities
for two spins 1/2

13. Quantum mechanics
Adding spins 1/2
Triplet
possibilities
Singlet

14. Adding spins 1/2 Triplet Singulet Quantum mechanics
Magnitude of the spin momentum ?
Triplet
Singulet

15. Adding spins S Pb 4.34, 4.35 Quantum mechanics
Possible values for S:
Clebsch- Gordan coefficients
Pb 4.34, 4.35

16. Quantum mechanics
Clebsch- Gordan coefficients

17. What is the value of the Clebsch-Gordan coefficient ?
Quantum mechanics
Quiz 29b
What is the value of the Clebsch-Gordan coefficient ? A. B. D. E.

18. The spin and magnetic field
Quantum mechanics
The spin and magnetic field S

19. The spin and magnetic field
Quantum mechanics
The spin and magnetic field S B

20. Larmor precession B S Pb 4.32 Larmor frequency Quantum mechanics z a yx y S
Pb 4.32
Larmor frequency

21. Stern-Gerlach experiment
Quantum mechanics
Stern-Gerlach experiment z B S
Moves down
Moves up