Radiation in Atoms

Now we will go all the way back to **Plank** who proposed that the emission of radiation be in quanta with
to solve the problem of Black Body Radiation.
So far, in our treatment of atoms, we have not included the possibility to **emit or absorb real photons**nor have we worried about the fact that Electric and Magnetic fields are made up of virtual photons.
This is really the realm of Quantum Electrodynamics, but we do have the tools to understand what happens as we quantize the EM field.

We now have the solution of the Harmonic Oscillator problem using operator methods.
Notice that the **emission of a quantum of radiation** with energy of
is
**like the raising of a Harmonic Oscillator state**.
Similarly the absorption of a quantum of radiation is like the lowering of a HO state.
Plank was already integrating over an infinite number of photon (like HO) states, the same integral we would do if we had an infinite number
of Harmonic Oscillator states.
Plank was also correctly counting this infinite number of states to get the correct Black Body formula.
He did it by considering a cavity with some volume, setting the boundary conditions, then letting the volume go to infinity.

This material is covered in **Gasiorowicz Chapter 22,**
in **Cohen-Tannoudji et al. Chapter XIII,**and briefly in Griffiths Chapter 9.

- The Photon Field in the Quantum Hamiltonian
- Decay Rates for the Emission of Photons
- Phase Space: The Density of Final States
- Total Decay Rate Using Phase Space
- Electric Dipole Approximation and Selection Rules
- Explicit 2p to 1s Decay Rate
- General Unpolarized Initial State
- Angular Distributions
- Vector Operators and the Wigner Eckart Theorem
- Exponential Decay
- Lifetime and Line Width

- Phenomena of Radiation Theory

- Examples

- Derivations and Computations
- Energy in Field for a Given Vector Potential
- General Phase Space Formula
- Estimate of Atomic Decay Rate

- Homework Problems
- Sample Test Problems