Gebrehiwot, Markos (2011) Quantum Dynamics of Atomic Electrons. Masters thesis, Addis Ababa University.
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Abstract
In this Thesis we study the Quantum Dynamics of Atomic Electrons. Using the mathematical derivation of the system of two coupled differential equations for the radial wave function, we have calculated the Sommerfeld expression for energy eigenvalues for electrons bound to nuclei. Then we have calculated the wave function at the diving point. Applying the Sommerfeld-fine structure formula, we have calculated the binding energies for 1s1=2. And we have classified the bound states of the electron according to the Dirac equation for Z = 1 (hydrogen atom). We found that the energy levels descend progressively with increasing Z. The energy of the lowest state (1s; k = 1) becomes negative when the nuclear charge Z > 150 and 1s level finally reaches the values E1s = −m0c2 at a critical charge Zcr 1s ’ 173. Hence the Sommerfeld energies of the states with k = −1(ns1=2) and k = +1(np1=2) break off with a vertical tangent at Zα = 1 and with the finite nuclear radius taken into account all levels reach the edge of the lower continuum E = −m0c2 at a corresponding critical charge Zcr. Using perturbation potential V 0 we have determined the Fano’s formalism for the description of resonances. And using Fano’s formalism we have calculated the final hole probability in the bound state and the spectrum of the emitted positrons depending on the diving duration. Then, we found that the modified continuum wave ΨE(r) thus displays exactly the same asymptotic behavior as E(r) but it is shifted by an angle ∆E. The probability of finding a hole in state φ0 after a time T thus decreases exponentially as determined by the decay width Γ0 = ΓEr. An oscillating function with maximum at E = E r having a width decreasing with the inverse of T. The peak height increases quadratically and it consistent linearly in T until saturation is reached at T > 1=Γ0.
| Item Type: | Thesis (Masters) |
|---|---|
| Subjects: | Q Science > Q Science (General) Q Science > QC Physics |
| Divisions: | Africana |
| Depositing User: | Selom Ghislain |
| Date Deposited: | 19 Nov 2018 12:56 |
| Last Modified: | 19 Nov 2018 12:56 |
| URI: | http://thesisbank.jhia.ac.ke/id/eprint/7312 |
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