Search

The hydrogen atom is a fundamental system in quantum mechanics that has been extensively studied due to its simplicity and relevance to atomic physics. The accurate determination of the energy levels of the hydrogen atom is of paramount importance for various applications in physics and chemistry. Hence, the objective of this work is to solve the fourth-order generalized Schrodinger problem for the hydrogen atom using the Frobenius series application. Findings obtained demonstrate the effectiveness and efficiency in determining the energies of the hydrogen atom, thereby contributing to a deeper understanding of quantum mechanical systems. [ABSTRACT FROM AUTHOR]

The exact solution for the gravitational potential field and gravitational intensity field for spherical bodies in three homogeneous regions are calculated using the method of variable separation. Our results showed that the gravitational potential field in the second region and that in the third region for two homogeneous and three homogeneous regions respectively are not linear but that in the third region shows more curve. The gravitational intensity field for the two homogenous regions is less than the gravitational intensity field for the three homogenous regions. The results of the gravitational intensity field for the three homogenous regions is closer to the experimental value showing that the present result is more valid. [ABSTRACT FROM AUTHOR]