The solution of the Dirac equation for a massive spin ½ particle in a Yukawa-type potential is investigated by transforming the radial form of the Dirac equation into the Whittaker equation from which we have obtained the desired solutions for the regions near the boundaries of the upper and lower energy continuum, E ≈ ∓ m. Comparison is made with earlier studies.
In the present work, genetic algorithm method (GA) is applied to the problem of impurity at the center of a spherical quantum dot for infinite confining potential case. For this purpose, any trial variational wave function is considered for the ground state and energy values are calculated. In applying the GA to the problem under investigation, two different approaches were followed. Furthermore, a standard variational procedure is also performed to determine the energy eigenvalues. The results obtained by all methods are found in satisfactory agreement with each other and also with the exact values in literature. But, it is found that the values obtained by genetic algorithm based upon wavefunction optimization are closer to the exact values than standard variational and also than genetic algorithm based on parameter optimization methods.
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