1. Physics 451 Quantum mechanics I Fall 2012 Nov 5, 2012 Karine Chesnel

2. Homework this week: HW #17 Tuesday Nov 6 by 7pm HW #18 Thursday Nov 8 by 7pm Announcements Quantum mechanics

3. The hydrogen atom What is the density of probability of the electron?

4. The hydrogen atom The angular equation (same) Angular function (same) Azimutal quantum number Magnetic quantum number l m Phys 451

5. The radial equation The hydrogen atom Coulomb’s law: Phys 451

6. Asymptotic behaviors The hydrogen atom The radial equation Phys 451

7. The hydrogen atom Peeling off the asymptotic behaviors Power expansion Recursion formula: Phys 451

8. The hydrogen atom The series must terminate Principal quantum number Phys 451

9. Quantum mechanics Quiz 23a A. one B. two C. n D. n -1 E. An infinity For a given quantum number n, how many values of l can exist?

10. Quantum mechanics The hydrogen atom Ground state: “binding energy” Quantization of the energy Bohr 1913 Principal quantum number

11. Quantum mechanics The hydrogen atom Bohr radius

12. Quantum mechanics The hydrogen atom Energies levels Stationary states n: principal quantum number l: azimuthal quantum number m: magnetic quantum number Degeneracy of n th energy level:

13. Quantum mechanics Quiz 23b A. 5 B. 9 C. 11 D. 25 E. 50 What is the degeneracy of the 5 th energy band of the hydrogen atom?

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