Efficiency of genetic algorithm and determination of ground state energy of impurity in a spherical quantum dot

TL;DR

This paper applies genetic algorithms to calculate the ground state energy of an impurity in a spherical quantum dot, demonstrating that wavefunction optimization yields more accurate results than parameter optimization or standard variational methods.

Contribution

It introduces a genetic algorithm approach for wavefunction optimization in quantum dot impurity problems, showing improved accuracy over traditional methods.

Findings

Genetic algorithm results closely match exact values.

Wavefunction optimization outperforms parameter optimization.

All methods show satisfactory agreement with literature values.

Abstract

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.