A scheme of numerical solution for three-dimensional isoelectronic series of hydrogen atom using one-dimensional basis functions

The solution of three-dimensional Schrödinger wave equations of the hydrogen atoms and their isoelectronic ions (Z = 1 − 4) are obtained from the linear combination of one-dimensional hydrogen wave functions. The use of one-dimensional basis functions facilitates easy numerical integrations. An iteration technique is used to obtain accurate wave functions and energy levels. The obtained ground state energy level for the hydrogen atom converges stably to −0.498 a.u. The result shows that the novel approach is efficient for the three-dimensional solution of the wave equation, extendable to the numerical solution of general many-body problems, as has been demonstrated in this work with hydrogen anion.