The first excited state of the hydrogen atom and the golden ratio: a link or a mere coincidence?

Authors

  • Vladimir M. Petruševski Institute of Chemistry, Faculty of Natural Sciences and Mathematics, Ss. Cyril & Methodius University, Skopje,

DOI:

https://doi.org/10.20450/mjcce.2006.281

Keywords:

science education, philosophy, hydrogen, quantum mechanics, golden mean

Abstract

The hydrogen atom is one of the systems for which (ignoring the electron spin) the Schrödinger equation can be solved exactly. The solutions of the radial part of the equation are usually given in terms of functions related to the associated Laguerre polynomials. Unexpectedly, the extremes (two maxima shared by a minimum) of the radial distribution function are related to the golden ratio (j). It is quite possible that this finding is a mere coincidence, rather than a consequence of the ‘eternal harmony of Nature’ or ‘the divine principle of beauty’ etc., but still it is interesting to point to the existence of the above link.

References

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H. Walser, The Golden Section, The Mathematical Association of America (translation from German), 2001, pp. 1–142.

V. M. Petruševski, S. M. Kalajdžievski, M. Ž. Najdoski, Quasicrystals: Comparison with Crystals, Construction of 2D Lattices and Demonstrations Using a Laser Pointer, Chem. Educator, 8, 358–363 (2003).

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http://goldennumber.net/ (accessed November 23rd, 2005).

V. M. Petruševski, The H-atom and the golden ratio: A possible link?, J. Chem. Educ. (in press).

P. W. Atkins, Physical Chemistry (5th edition), Oxford University Press, Oxford, 1994, pp. 421–460.

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Published

2006-06-15

How to Cite

Petruševski, V. M. (2006). The first excited state of the hydrogen atom and the golden ratio: a link or a mere coincidence?. Macedonian Journal of Chemistry and Chemical Engineering, 25(1), 61–63. https://doi.org/10.20450/mjcce.2006.281

Issue

Vol. 25 No. 1 (2006)

Section

Education

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