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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/3637

Title: Quantum Dynamics of Atomic Electrons
Authors: Gebrehiwot, Markos
Advisors: Dr. Bhatnagar S.
Keywords: Atomic Electrons
Quantum Dynamics
Copyright: Jun-2011
Date Added: 6-Nov-2012
Publisher: AAU
Abstract: In this Thesis we study the Quantum Dynamics of Atomic Electrons. Using the mathematical derivation of the system of two coupled di erential 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- ne structure formula, we have calculated the binding energies for 1s1=2. And we have classi ed 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 nally reaches the values E1s = 􀀀m0c2 at a critical charge Z1s cr ' 173. Hence the Sommerfeld energies of the states with k = 􀀀1(ns1=2) and k = +1(np1=2) break o with a vertical tangent at Z = 1 and with the nite 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 nal hole probability in the bound state and the spectrum of the emitted positrons depending on the diving duration. Then, we found that the modi ed continuum wave E(r) thus displays exactly the same asymptotic behavior as E(r) but it is shifted by an angle E. The probability of nding a hole in state 0 after a time T thus decreases exponentially as determined by the decay width 􀀀0 = 􀀀Er . An oscillating function with maximum at E = Er 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=􀀀0.
Description: A Thesis Submitted to the School of Graduate Studies Addis Ababa University In Partial Fulfillment of the Requirement for the Degree of Master of Science in Physics
URI: http://hdl.handle.net/123456789/3637
Appears in:Thesis - Physics

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