Least‐squares fitting of parametrized Hamiltonians to energy levels: An investigation into alternative strategies

Many phenomenological models involve fitting parametrized Hamiltonians to experimentally determined energy levels. It is not uncommon to obtain highly deviant sets of parameters. While this may be due to poor empirical data, it can also result from the use of unstable least‐squares fitting procedures. A specific example is examined in some detail, and it is shown that the instabilities inherent in the standard approach can be easily overcome. An optimal strategy is proposed.