WSEAS

Abstract: Quantum Optimal Control Problems are encountered in many fields of physics, chemistry and a lot of applied sciences and their mathematical background and tools are quite rich in nature. Since the most of the cost functionals used in these problems are beyond the quadratic nature, the variationally obtained control equations are nonlinear partial differential equations coupled with one or more functional equations. The character of the motion corresponds to a boundary value problem in time. The solution of these equations can be obtained through various standing methods. One of the recently developed methods to this end is based on the expectation values of certain quantum mechanical operators. Instead of the wavefunction's evolution, these expectation values' evolution is taken into consideration. The result is a set of coupled ordinary differential equations with nonliearities both in the structure and in the accompanied boundary conditions. Nevertheless they are ordinary differential equations and there is an abundance of methods to solve them. This presentation will cover the mainlines and important aspects of this approach after an introductory historical development section. Most recent applications will also be mentioned.