The angular part of the Schrödinger equation for the hydrogen atom

James M. Feagin

G. Richard Fowles

A.B. Datzeff

Mohammad Reza Pahlavani, Hossein Rahbar, Mohsen Ghezelbash

In this investigation a simple method developed by introducing spin to Schrodinger equation to study the relativistic hydrogen atom. By separating Schrodinger equation to radial and angular parts, we modify these parts to the associated Laguerre and Jacobi differential equations, respectively. Bound state Energy levels and wave functions of relativistic Schrodinger equation for Hydrogen atom have been obtained. Calculated results well matched to the results of Dirac’s relativistic theory. Finally the factorization method and supersymmetry approaches in quantum mechanics, give us some first order raising and lowering operators, which help us to obtain all quantum states and energy levels for different values of the quantum numbers n and m.

Vinod Kumar Khanna

During the solution of the Schrodinger equation for the hydrogen atom by separation of variables, we come across three quantum numbers, namely the azimuthal quantum number l , the magnetic quantum number m l , and the principal quantum number n . The quantum number l arises as a separation constant during the breaking apart of radial and angular segments of the Schrodinger equation and the quantum number m l occurs while separating the azimuthal component from the polar component of the angular part. The quantum number n is necessary to render the series for the non-asymptotic part of the radial wave function convergent. The three quantum numbers are interdependent because after selecting n , the selection of l is restricted to allowed values and similarly after choosing l , limited values are permitted for m l . The fourth quantum number m s representing electron spin is not a direct consequence of solving the Schrodinger equation. The detailed solution procedure of the Schrodinger equation including the normalization of the wave function, restrictions on the values of quantum numbers, and allied analysis are explained.

Bambang Supriadi, Zainur Rasyid Ridlo, F Fuadah +3 more

The lightest and simplest arrangement of protons and electrons is a hydrogen atom. One of the wave characteristics of an atom can be known using the Schrodinger equation. Schrodinger's equations of spherical coordinates consist of radial equations and angular equations. Quantum numbers 4≤ n ≤ 5from the Schrodinger equation sphere coordinates produce different angular wave functions. To find out the angular wave equation using normalization conditions . Based on the normalization conditions for n = 4 a wave function is produced , while for n = 5 a wave function is .