Wave functions of higher dimensional hydrogen atom. Its algebraic derivation, graphic representation, and physical meaning

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In our previous research we have derived the general formula of the degeneracy of the angular part of the n-dimensional atomic hydrogen wave functions, which can be obtained recursively by simple manipulation of the famous Pascal's triangle. The essence of our findings is in its algebraic and heuristic method without recourse to analytical and sophisticated techniques for solving the Schrodinger equation but from the algebraic relations among the existing analytical solutions.In this research project 1) we have succeeded in establishing the animation technique for drawing various facets of the cross sections of n-dimensional atomic orbitals projected on the lower dimensional coordinate systems. 2) With this technique a number of cross sections were obtained for ordinary 3-dimensional atomic orbtials of s-, p-, and d-types, which, however, have not been available in the quantum chemistry textbooks. 3) With this experience in mind a number of cross sections of 4-dimensional atomic orbitals were drawn, enabling easy understanding of the analytical and geometrical structure of the atomic orbital wavefunctions of the whole family of the n-dimensional world. 4) By assembling the newly obtained information on the n-dimensional atomic orbitals the secret of the interesting relation between the degeneracy of these orbitals and the asymmetrical Pascal's triangle.As a whole the obtained results in this research project could provide new and exciting information and insight not only for graduate students but also for active researchers in chemistry and physics.