Saito Group (Open)
Started by Thomas.2013.09.02
This is Thomas's logbook for September of 2013.
1st week [Electron-Photon Interactions] †
- The Hamiltonian for the electron-photon interaction is given by , in this equation is the linear momentum, is the charge of the particle, is the vector potential, is the particle's mass, is the speed of light and is the scalar potential. It is possible to check this by using the canonical equations from Hamilton, and .
- From those last equations together with the following identities and With all this considered it was possible to arrive at the equation of motion of a particle under an electromagnetic field, .
- Consider the wave functions from quantum well, hydrogen atom, and solve with the electromagnetic(electron-photon interaction) perturbation.
- By looking at the previous Hamiltonian in a different shape, where the term inside the brackets is actually the unperturbed hamiltonian, and the other terms are the perturbations that arise from the electomagnetic field influence.
- As the electromagnetic field is just a perturbation, it is not so strong, therefore it is possible to disregard , and consider the perturbation Hamiltonian as .
- Taking a monochromatic wave over a quantum well of length it is possible to find the new wavefunction after taking the .
- Find the actual new wavefunctions.
- Following the condition for finding the perturbation result. The wave equations for the states , initial (), and , final (), are considered. Also for the perturbation, the Coulomb gauge will be chosen, , as a result, the perturbation Hamiltonian will be .
- So, with and which would be .
- Evaluate other transitions, in order to get the linear combination which it is the new wavefunction.
- After evaluating the the result was . The and are null.
2nd week [Raman Spectroscopy Book, Chapter 5 Exercises] †