Authors : Hossein Parsian and Reza Sabzpoushan
Abstract: Wavelets constitute a family of functions that constructed from dilation and translation of a single function. They are suitable tools for solving variational problems. In this study, we want to extremum the Hamiltonian of hydrogen atom using Legendre wavelets. Legendre wavelets are defined on the domain [0,1]. For solving this problem, we represent a generalized Legendre functions and generalized Legendre wavelets on the [-s, s] and [0, s], respectively. We start from the radial equations of hydrogen atom like and represent the wave function in term of generalized Legendre function and then convert the redial equation of hydrogen atom like to a polynomial in term of coefficients of wave function. The eigenstate will be minimize provided that, the derivative of it respect to the all of coefficients of wave function to be equal zero. The last equation is a algebraic equation and the solutions are the energy states of hydrogen atom like.
Hossein Parsian and Reza Sabzpoushan , 2006. A Numerical Solution for Hydrogen Atoms Like. Asian Journal of Information Technology, 5: 951-954.