1: | Thursday | Apr 17, 2008 | 13:45-15:45 | HG03.632 | Zare 1.1, 1.2, 1.3 |

2: | Thursday | Apr 24, 2008 | 13:45-15:45 | HG02.702 canceled | |

3: | Tuesday | Apr 29, 2008 | 13:45-15:45 | HG03.054 | |

4: | Friday | May 2, 2008 | 13:45-15:45 | HG03.044 | Zare 2.1 and 2.2 |

5: | Thursday | May 8, 2008 | 13:45-15:45 | HG01.057 | Zare 3.1-3.4 |

6: | Thursday | May 15, 2008 | 13:45-15:45 | HG03.632 | Zare 3.5 |

7: | Thursday | May 22, 2008 | 13:45-15:45 | HG02.702 | Zare 3.7, 3.8, and 3.9 |

8: | Thursday | May 29, 2008 | 13:45-15:45 | HG03.632 | Zare 4.1 |

9: | Thursday | Jun 5, 2008 | 13:45-15:45 | HG03.082 | Zare 5.1 and 5.2 |

10: | Thursday | Jun 12, 2008 | 13:45-15:45 | HG03.082 | Zare 5.3 and 5.4 |

11: | Thursday | Jun 19, 2008 | 13:45-15:45 | HG03.082 | |

12: | Thursday | Jun 26, 2008 | 13:45-15:45 | HG03.082 | |

13: | Thursday | Jul 3, 2008 | 13:45-15:45 | HG03.082 | |

14: | Friday | Aug 22, 2008 | 13:45-15:45 | HG03.054 | Multipole expansion |

15: | Tuesday | Aug 26, 2008 | 13:45-15:45 | HG03.054 | Alignment parameters |

16: | Wednesday | Sep 24, 2008 | 13:45-15:45 | HG | Mo and Suzuki paper, photodissociation |

17: | (Wednesday) | (Oct 1), 2008 | (15:45-17:00) | (HG 2.702) | Op verzoek naar vrijdag middag verplaatst |

- official description of this course
- Lecture notes (pdf)
- Scilab routines for 3-j, 6-j, and 9-j symbols
- Notes on the multipole expansion (pdf)

- April 1st, 2007 (pdf)
- April 10, 2007 (pdf)

- Derive Eq. (50) using Eqs. (29) and (30)
- To derive Eq. (51) first show that L=l+1
- Show that the first Clebsch-Gordan coefficient in Eq. (50) must be 1 for mu=1 and m=l
- To derive the expression for the second CG coefficient, use the CG recursion relations to find an explicit expression for < 1 1 l m | l+1 m+1 >
- Next use the recursion relations to find < 1 0 l 0 | l+1 0 >
- Check Eqs. (51) and (52). Note that n!! = n (n-2) (n-4) ...
- Check Eqs. (53), (54), (55), (60), and (61)
- Derive Eq. (85) for M=L starting with Eq. (60)
- use binomial expression for (x+y)^l for x=R_1 and y=r_1
- to simplify the result use: (2n)! = (2n)!! (2n-1)!! = 2^n n! (2n-1)!! (check this)

- If Eq. (85) holds for M=L, why must it hold for all M?
- Equation (87) follows easily from the generating function of the Legendre
polynomials. Alternatively:
- Assume the function can be expanded in products of spherical harmonics of the polar angles of the vectors r and R and coefficients that only depend on then lengths of the vectors.
- Require the function to be invariant under simultaneous rotation of the vectors, and use the explicit expression for < l1 m1 l2 m2 | 0 0 >, Eq. (35), and the spherical harmonic addition theorem to write the function as a Legendre expansion.
- Show that P_l(1)=1
- Show that 1/(1-x)=1+x+x^2+x^3+...
- To find the expansion coefficients consider the case where the angle between the vectors is zero.

- Check Eqs. (88), (89), and (90).
- Introduce the multipole operators [Eq. (78)] to write down the multipole expansion of the Coulomb interaction between two molecules.

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