The h index was introduced by Hirsch to quantify an individual's scientific research output. It has been widely used in different fields to show the relevance of the research work of prominent scientists. I have worked out 26 practical cases of physicists which are not so prominent. Therefore this case study should be more relevant to discuss various features of the Hirsch index which are interesting or disturbing or both for the more average situation. In particular, I investigate quantitatively some pitfalls in the evaluation and the influence of self-citations.