Stationary Perturbation Theory

Abstract

The description of any physical system is only approximate. It is true, of course, that it is possible to solve some models exactly, but such models in turn only approximately describe real physical systems. For example, the harmonic oscillator describes a vibrating diatomic molecule only when the vibrations are not too violent and anharmonic forces are negligible. In a similar vein, it is possible to find the energy levels of the hydrogen atom using the appropriate non-relativistic Hamiltonian. But the non-relativistic Hamiltonian or Schrodinger equation is only approximate: to take into account the spin of the electron, the Pauli equation or Pauli Hamiltonian must be used to describe the electron. The Dirac equation is a relativistic equation that describes a spin-1/2 particle. To take into account the fact that electromagnetic signals travel between the proton and electron at the speed of light instead of instantaneously, the Bethe-Salpeter equation is employed. Even when the electron is traveling at speeds far less than that of light, the electron interacts electromagnetically with itself, causing small but experimentally detectable deviations from the energy levels calculated from the Pauli equation or Pauli Hamiltonian. Problems in physics cannot usually be solved exactly. Therefore, if a physicist wishes to calculate numbers that can be compared with experimental values, approximations are inevitable.