Thomas-September Progress (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! cURL: Could not resolve host: chart.apis.google.com;, in this equation &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; is the linear momentum, &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; is the charge of the particle, &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; is the vector potential, &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; is the particle's mass, &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; is the speed of light and &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; is the scalar potential. It is possible to check this by using the canonical equations from Hamilton, &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; and &tex(): Error! cURL: Could not resolve host: chart.apis.google.com;.

From those last equations together with the following identities &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; and &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; With all this considered it was possible to arrive at the equation of motion of a particle under an electromagnetic field, &tex(): Error! cURL: Could not resolve host: chart.apis.google.com;.

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! cURL: Could not resolve host: chart.apis.google.com; 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! cURL: Could not resolve host: chart.apis.google.com;, and consider the perturbation Hamiltonian as &tex(): Error! cURL: Could not resolve host: chart.apis.google.com;.

Taking a monochromatic wave over a quantum well of length &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; it is possible to find the new wavefunction after taking the &tex(): Error! cURL: Could not resolve host: chart.apis.google.com;.

09.04
- Following the condition for finding the perturbation result. The wave equations for the states &tex(): Error! cURL: Could not resolve host: chart.apis.google.com;, initial (&tex(): Error! cURL: Could not resolve host: chart.apis.google.com;), and &tex(): Error! cURL: Could not resolve host: chart.apis.google.com;, final (&tex(): Error! cURL: Could not resolve host: chart.apis.google.com;), are considered. Also for the perturbation, the Coulomb gauge will be chosen, &tex(): Error! cURL: Could not resolve host: chart.apis.google.com;, as a result, the perturbation Hamiltonian will be &tex(): Error! cURL: Could not resolve host: chart.apis.google.com;.

So, &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; with &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; and &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; which would be &tex(): Error! cURL: Could not resolve host: chart.apis.google.com;.

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

09.05
- After evaluating the &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; the result was &tex(): Error! cURL: Could not resolve host: chart.apis.google.com;. The &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; and &tex(): Error! cURL: Could not resolve host: chart.apis.google.com; are null.