ON THE DERIVATION OF BOUND STATE WAVEFUNCTIONS OF HYDROGEN ATOM USING PARABOLIC COORDINATES
Abstract
In this article, we introduce a rigorously mathematical procedure to analytically derive the bound state wavefunctions of hydrogen atom by utilization of parabolic coordinates. The general form of the bound state wavefunctions in these coordinates is presented, then the transformation of wavefunctions from parabolic coordinates to well-known spherical coordinates for states with principle quantum number n = 1 and 2 is also considered for validating our calculation.References
Abramowitz M. and Stegun I. A., “Handbook of Mathematical Functions”, Dover Publications, New York (1972).
Bethe H. A. and Salpeter E. E., “Quantum Mechanics of One- and Two- Electron Atoms”, Springer-Verlag, Berlin (1957).
Fernández-Menchero L. and Summers H. P., “Stark effect in neutral hydrogen by direct integration of the Hamiltonian in parabolic coordinates”, Physical Review A 88 (2013), 022509.
Landau L. D. and Lifshiz E. M., “Quantum Mechanics (Non-relativistic Theory”, Pergamon Press, Oxford (1977).
Morse M. P. and Feshbach H., “Method of Theoretical Physics”, McGraw-Hill Book Company Inc., Newyork (1953).
Pham Vinh N. T., Tostikhin Oleg I., and Morishita Toru, “Molecular Siegert states in an electric field. II. Transverse momentum distribution of the ionized electrons”, Physical Review A 89 (2014), 033426.
Stodona A. S., Rouzee A., Lepine F., Cohen S., Robicheaux F., Gijsbertsen A., Jungmann J. H., Bordas C., and Vrakking M. J. J., Hydrogen Atoms under Magnification: Direction Observation of the Nodal Structure of Stark States”, Physical Review Letter 110 (2013), 213001.
