Bound States in the Dirac Equation
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Date
2000-06
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Addis Ababa University
Abstract
In this thesis the framework of Dirac equation has been exploited to make a detailed
study on the relativistic bound state features of Hydrogen-like atoms. The relativistic
energy eigenvalues calculated in this framework show the evidence of fine structure
splitting for various levels. The origin of this feature can be traced to the relativistic
calculations and the spin of the electron. The interesting features of these results
are that the bound states are observed to lie in the forbidden gap between
-111
0c2 s Es +1110 c2
• For the attractive coulomb potential used in this work the bound
states were observed to start from just below the positive energy continuum (E<O).
The possibility of the existence of bound states even for repulsive potential was also
observed provided we give up the single particle interpretation. Such bound sates
for repulsive potential start from just above the lower negative energy continuum.
The non-relativistic limit (1110c2 >> JficJ) of the Dirac equation has also been
investigated in this thesis. We observe that even in this approximation the Dirac
equation is able to generate the exact form of the spin-orbit interaction term. We
have also exploited the non-relativistic approximation of the Dirac equation to work
out the value of the electron magnetic moment
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The Dirac Equation