1. Physics 451 Quantum mechanics I Fall 2012 Nov 12, 2012 Karine Chesnel

2. Announcements Quantum mechanics Homework this week: HW #19 Tuesday Nov 13 Pb 4.14, 4.15, 4.16, 4.17 HW #20 Thursday Nov 15 Pb 4.18, 4.19, 4.21, 4.22 Test 3 Review Monday Nov 19- 20 Sign for practice test

3. Quantum mechanics The angular momentum Ladder operator Top Value =+l Bottom Value = -l Eigenstates

4. Quantum mechanics The angular momentum Pb 4.18

5. Quantum mechanics The angular momentum In spherical coordinates x y z r

6. Quantum mechanics The angular momentum In spherical coordinates x y z r Pb 4.21, 4.22

7. Quantum mechanics The angular momentum eigenvectors x y z r and were the two angular equations for the spherical harmonics! Spherical harmonics are the eigenfunctions

8. Quantum mechanics The angular momentum and Schrödinger equation x y z r 3 quantum numbers (n,l,m) Principal quantum number n: integer Azimutal and magnetic quantum numbers (l,m) can also be half-integers.

9. Quantum mechanics Quiz 26 A. 0 B. C. D. E. For a given n value, how many eigenstates can we find for the operator ?

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

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

12. 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 Mesons Photon S=1

13. Quantum mechanics The spin

14. Quantum mechanics The spin

15. Quantum mechanics The spin 1/2 The “spinor” Spin upSpin down

16. Quantum mechanics Pauli matrices Pb 4.29