Laguerre Polynomials, Reminiscences from Uppsala
I joined Professor Löwdin’s group in Uppsala as a young chemistry student from Hungary in the summer of 1957. The first couple of months I spent doing odd jobs in the office like pasting Physics Abstract cuttings on sheets of white paper and helping the secretaries with the binding of Technical Reports. In the meantime I was busy reading Löwdin’s articles trying to learn and understand his approach to quantum chemistry. After a few months Professor Löwdin decided that I might have made enough progress to be given a problem. It was on the ground state of the Helium atom, where extensive use was to be made of Laguerre polynomials. At this time Professor Löwdin had put strong emphasis on the importance of using a complete set of base functions like Laguerre polynomials rather than e.g. bound state hydrogen-like wave functions which are not complete unless the continuum states are also included /l/. I was supposed to use the variational method. This was my first research problem and I started to work on it with great enthusiasm. After calculating matrix elements for three months I got to the stage of putting it on the computer. To my horror and surprise the result of the first run was far below the experimental value of the ground state energy. Inexperienced as I was, even I had realized that something must have gone wrong.