The objective of this monograph is to present the most advanced topics in analysis of mathematical structure in Schrödinger equations. Quantum science becomes important in recent years because we need industrial and electronic applications of microscopic phenomena in quantum computation, quantum communication, and quantum cryptography etc. It is also expected in future that computer scientists apply the result in fundamental theory to the development of quantum devices like quantum computers. The exciting results will be of interest to researchers, graduate and undergraduate students in...