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

- 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.

- 09.04
- Following the condition for finding the perturbation result. The wave equations for the states &tex(): Error! The expression contains invalid characters.;, initial (&tex(): Error! The expression contains invalid characters.;), and &tex(): Error! The expression contains invalid characters.;, final (&tex(): Error! The expression contains invalid characters.;), are considered. Also for the perturbation, the Coulomb gauge will be chosen, &tex(): Error! The expression contains invalid characters.;, as a result, the perturbation Hamiltonian will be &tex(): Error! The expression contains invalid characters.;.

- So, &tex(): Error! The expression contains invalid characters.; with &tex(): Error! The expression contains invalid characters.; and &tex(): Error! The expression contains invalid characters.; which would be &tex(): Error! The expression contains invalid characters.;.

- Next Steps:

- Evaluate other transitions, in order to get the linear combination which it is the new wavefunction.

- 09.05
- After evaluating the &tex(): Error! The expression contains invalid characters.; the result was &tex(): Error! The expression contains invalid characters.;. The &tex(): Error! The expression contains invalid characters.; and &tex(): Error! The expression contains invalid characters.; are null.

Last-modified: 2013-09-13 (Fri) 11:00:11