Introduction and Overview (2): Approximations and Calculation Techniques in Quantum Theory

Now we are going to focus on the approximation techniques of solving the Schrödinger equation and some other crucial equations that determine the behavior of a quantum system. Most of them are grounded on a similarity of the considered problem with some well-known and easily solvable problems, while some others require an educated guess on the unknown properties of a particle. We are going to discuss different approximation methods used in many-electron physics including the density functional theory. It is amazing to see how standard calculation approaches studied in quantum mechanics are successfully employed in cutting-edge research problems, which will be addressed in detail in this chapter. Developing, formulating, and applying novel approximation methods, including the WKB, for new quantum systems remains one of the most actively explored directions in theoretical physics that will never lose its importance.