Among the subjects reviewed in these Advances, the properties and computation of electromagnetic fields have been considered on several occasions. In particular, the early work of H.F. Harmuth on Maxwell's equations, which was highly controversial at the time, formed a supplement to the series This volume, unlike previous volumes in the series concentrates solely on the research of professors' Harmuth and Meffert. These studies raise important and fundamental questions concerning some of the basic areas of physics: electromagnetic theory and quantum mechanics. They deserve careful study and reflection for although the authors do not attempt to provide the definitive answer to the questions, their work is undoubtedly a major step towards such an answer. This volume essential reading for those researchers and academics working applied mathematicians or theoretical physics Unlike previous volumes, this book concentrates solely on the new research of professors Harmuth and Meffert Raises important and fundamental questions concerning electromagnetism theory and quantum mechanics Provides the steps in finding answers for the highly debated questions.