1. Hydrogen Atom
PHY 361

2. Outline review of Lz spherical coordinates
operator, eigenfunction, eigenvalues
rotational kinetic energy
traveling and standing waves
spherical coordinates
definition
Laplacian operator
Schrödinger’s equation in spherical coordinates
separation of angular variables:
L2 and Lz differential equations
spherical harmonics and eigenvalues
vector model of quantum angular momentum
radial wavefunctions
effective radial potential – centrifugal `force’
radial wave functions
hydrogenic orbitals
I will start with a brief reminder of where we were last, and explain the different options available for polarizing the beam. Then I will go on and show the progress we have made towards a feasible design of the novel splitter polarizer geometry. We have also done new detailed simulations of the different designs and recalculated the costing of each for comparison. Based on this new information, we have arrived at a choice for the baseline design.

3. Spherical Coordinates

4. Cylindrical vs. Spherical Coordinates
Laplacian:
Schrödinger Equation:
Lz2 / 2I
L2 / 2I

5. Spherical Harmonics L2 Ylm=l(l+1)Ylm Lz Ylm= m Ylm s 1 x, y p z x, y
x2+y2, xy
xz, yz d
3z2-1
xz, yz
x2+y2, xy
f …

6. Vector model of quantized angular momentum
m = -1, -l+1, … l-1, l

7. Potential energy function and bound states

8. Radial equation – effective potential

9. Radial hydrogenic wavefunctions

10. Putting radial and angular parts together
2p wave

11. Ground state wavefunction

12. Hydrogenic orbitals

13. Selection rules and transitions
difference in energy states measured from atomic transitions – E = h f
atomic spectroscopy
only certain transitions are allowed