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

#### 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.

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