Mathematical remarks on the optimized effective potential problem. (Q873229)

Optimal effective potential (OEP) problem---minimization problem from computational chemistry is analyzed. In order to obtain rigorous results, several assumptions substantially constraining the original OEP problem are made. (For example molecular system with only two electrons is considered etc.) As a result, only somewhat academic cases are studied, laying, however, rigorous foundations for further more general works. A weak formulation of the (simplified) OEP problem is presented and it is shown to be well posed. Various related problems are also analyzed.