Approximation Methods

The problems that can be exactly solved in quantum mechanics can be counted on the fingers of one hand. They include problems with piecewise constant potentials, the harmonic oscillator, the hydrogen atom, and a few others. By “exactly solving a problem” here, we mean the exact diagonalization of the Hamiltonian operator, i.e., the calculation of its eigenvalues and eigenkets. In the vast majority of cases, exact diagonalization is extremely complicated. In this chapter, we see how to approach these cases using methods that allow us to approximate the exact solution.