Review

particle in a box

contributions from famous quantum scientists

reduced mass

Bohr atom

de Broglie matter wave

photo-electron effect

Hermitian operator

commutator

hydrogen atom

harmonic oscialltor

ladder operator

angular momentum operator (lecture 18 - onwards)

classical understanding

• components of angular momentum (3 in cartesian plane) as cross product: $$L = r \times p = \begin{bmatrix} x & y & z \end{bmatrix} \times \begin{bmatrix} p_x & p_y & p_z \end{bmatrix} = \begin{bmatrix} i & j & k\\ x & y & z\\ p_x & p_y & p_z \end{bmatrix}$$

$$L = i(yp_z - p_yz) - j(xp_z - p_xz) + k(xp_y - p_xy) \\ = iL_x - jL_y + kL_z$$

• right handed coordinate system
• cyclic

commutation relationship

• coupling of angular momentum vectors in molecules
  • when axes are mounted on molecule, sign of i flips in commutation

term symbols

L - S coupling

equivalent and non-equivalent electrons

Hund’s rules

Questions

ch 9

• 42