Hydrogen Atom Wave Functions

Norman Henry March

Marc J. Goovaerts, Fernand Broeckx, P. E. Van Camp

Bambang Supriadi, Alex Harijanto, M Maulana +3 more

The simplest atom consisting of a proton and an electron is a hydrogen atom. The energy level and the probability of finding an electron in a hydrogen atom can be determined based on the function of radial wave. The function of radial wave of a hydrogen atom is influenced by the principal quantum number ( n ) and the orbital quantum number ( l ). Completion of the function of radial wave of a hydrogen atom in the principal quantum numbers( n ) 4 and 5 uses the time-independent Schrodinger equation approach in spherical coordinates, variable separation method and uses the associated Laguerre function. The normalized of the function of radial wave of a hydrogen atom R nl ( r ) at n = 4 produces four wave functions:R 40 ( r ); R 41 ( r ); R 42 ( r ); R 43 ( r ), whereas at n = 5 produces five wave functions:R 50 ( r ); R 51 ( r ); R 52 ( r ); R 53 ( r ); R 54 ( r ). The results of this research in the form of the functions of radial wave of hydrogen atom can be used to determine the behavior of electron in a hydrogen atom.

James W. Rohlf

The Bohr model is highly successful in explaining many features of the hydrogen atom. The ground state wave function does not have any angular dependence. The normalized hydrogen atom wave functions are directly accessible in Mathematica and can be readily verified as solutions of the Schrodinger equation. Get the hydrogen atom ground state wave function in terms of the Bohr radius a. The probability of finding the electron per volume at a given location is given by the square of the wave function. The electron has only a very tiny probability of being found inside the proton, whose size is about 1 fm.

Brian P. Anderson