2. Chapter Outline Single Particle SE for H-atom Angular Moment QN
H-atom Atomic Orbitals
Atomic Orbitals & Spectroscpy
Multielectron Systems

4. Single Particle Under Central Force
The Hamiltonian
No dependence on direction – spherically symmetric
PE depends only on position:
Single Particle Under Central Force
Reduced mass:
Approximate as a single particle system with the massive proton being fixed
Enter H-atom
We have a 2 particle system with 1 proton & 1 electron

6. Getting our DiffEq
SE for H-atom

7. Isolating R(r) & Y(,)
SE for H-atom

9. We get to our l QN when we apply
Angular Moment & QNs

11. H Atomic s & Orbitals Getting to En Hydrogen Atomic s Now for R(r)
First few  with Z = atomic #
H Atomic s & Orbitals
Now for R(r)

13. Recall the QNs
The Atomic Orbitals

14. The Atomic Orbitals Radial Distribution Plots
Nodes: location where the probability is zero
S-Orbitals
The max for 1s is located at a0
P-orbitals
m = 0 for –pz orbital
m =  1 for px & py orbitals
The Atomic Orbitals
d-Orbitals are similar

15. Skip!!! For now

17. Multi-electron Systems
The Problem
Multi-electron Systems
We can solve it exactly for 1 e- systems
We cannot get an analytic solution for more than 1 e-
We will discuss approximate/numeric solutions in Ch 8