History of Thomas-September Progress (Open) (No. 11)

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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)
  • 6 (2013-09-03 (Tue) 22:03:06)
  • 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)

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.

• 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.