The Stark effect in hydrogen

Student thesis: Master thesis (including HD thesis)

  • Joana Angelica Rodzewicz Sohnesen
4. term (FYS10), Physics, Master (Master Programme)
In the report the Stark effect for the ground state of a hydrogen atom is studied using perturbation theory. First parabolic coordinates are introduced for the hydrogen atom without an external electric field and the Schrödinger equation for movement of the electron in three and two dimensions respectively is solved analytically to find the energy and the eigenstates. Then the Schrödinger equation for the Stark effect is solved using perturbation theory. First the calculations are made for three and two dimensions. This is then generalised to noninteger dimension between 2 and 3 in order to describe a more realistic confinement of an electron in a nanostructure. A series for the energy as a function of the dimension and the applied electric field is found. The series is seen to be divergent which is explained by the tunnelling effect which leads to an ionisation of the atom. The eigenfunctions are used to plot the probability density which shows an expected asymmetry due to the electric field. Far away from the nucleus in the opposite direction of the applied field, large increases of the probability density are seen which are interpreted as a consequence of the tunnelling effect.
Publication date8 Jan 2016
Number of pages50
ID: 225516238