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Title:  Quantum Dynamics of Atomic Electrons 
Authors:  Gebrehiwot, Markos 
Advisors:  Dr. Bhatnagar S. 
Keywords:  Atomic Electrons Quantum Dynamics 
Copyright:  Jun2011 
Date Added:  6Nov2012 
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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