Saito Group (Open)

Started by Thomas.2013.09.02 This is Thomas's logbook for September of 2013.

## 1st week [Electron-Photon Interactions] †

• 09.02
• The Hamiltonian for the electron-photon interaction is given by &tex(): Error! The expression contains invalid characters.;, in this equation &tex(): Error! The expression contains invalid characters.; is the linear momentum, &tex(): Error! The expression contains invalid characters.; is the charge of the particle, &tex(): Error! The expression contains invalid characters.; is the vector potential, &tex(): Error! The expression contains invalid characters.; is the particle's mass, &tex(): Error! The expression contains invalid characters.; is the speed of light and &tex(): Error! The expression contains invalid characters.; is the scalar potential. It is possible to check this by using the canonical equations from Hamilton, &tex(): Error! The expression contains invalid characters.; and &tex(): Error! The expression contains invalid characters.;.
• From those last equations together with the following identities &tex(): Error! The expression contains invalid characters.; and &tex(): Error! The expression contains invalid characters.; With all this considered it was possible to arrive at the equation of motion of a particle under an electromagnetic field, &tex(): Error! The expression contains invalid characters.;.
• Next steps:
• Consider the wave functions from quantum well, hydrogen atom, and solve with the electromagnetic(electron-photon interaction) perturbation.
• 09.03
• By looking at the previous Hamiltonian in a different shape, &tex(): Error! The expression contains invalid characters.; 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 &tex(): Error! The expression contains invalid characters.;, and consider the perturbation Hamiltonian as &tex(): Error! The expression contains invalid characters.;.
• Taking a monochromatic wave over a quantum well of length &tex(): Error! The expression contains invalid characters.; it is possible to find the new wavefunction after taking the &tex(): Error! The expression contains invalid characters.;.
• Next Steps:
• Find the actual new wavefunctions.