1. Physics 451 Quantum mechanics I Fall 2012 Nov 20, 2012 Karine Chesnel

2. EXAM III Quantum mechanics Time limited: 3 hours Closed book Closed notes Useful formulae provided When: Monday Nov 26 – Fri Nov 30 Where: testing center

3. EXAM III Quantum mechanics 1. Schrödinger equation in spherical coordinates 2. Hydrogen atom: spherical harmonics 3. Hydrogen atom: radial function and energy 4. Electron’s spin and Pauli matrices 5. Spin and Magnetic field, Combination of two spins

4. Quantum mechanics Schrödinger equation in spherical coordinates

5. Quantum mechanics Schrödinger equation in spherical coordinates The angular equation The radial equation x y z r

6. Quantum mechanics The hydrogen atom Quantization of the energy Bohr radius

7. Quantum mechanics The hydrogen atom Energies levels Spectroscopy Energy transition Rydberg constant E 0 E1E1 E2E2 E3E3 E4E4 Lyman Balmer Paschen

8. Quantum mechanics x y z r Normalization Radial part angular part

9. Quantum mechanics The angular momentum eigenvectors x y z r Spherical harmonics are the eigenfunctions

10. Quantum mechanics The spin

11. Quantum mechanics Pauli matrices

12. Quantum mechanics Adding spins S Possible values for S when adding spins S 1 and S 2 : Clebsch- Gordan coefficients

13. EXAM II Quantum mechanics Some of the formulae provided Schrödinger equation Potential in hydrogen atom: and Bohr radius: Normalization Angular momentum

14. Quantum mechanics