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- 1 (2013-09-02 (Mon) 12:23:37)
- 2 (2013-09-02 (Mon) 12:28:01)
- 3 (2013-09-02 (Mon) 18:30:43)
- 4 (2013-09-02 (Mon) 20:42:57)
- 5 (2013-09-03 (Tue) 18:06:54)
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*7 (2013-09-04 (Wed) 12:48:15)*- 8 (2013-09-04 (Wed) 16:23:39)
- 9 (2013-09-04 (Wed) 22:33:52)
- 10 (2013-09-05 (Thu) 12:25:31)
- 11 (2013-09-05 (Thu) 16:08:56)

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.