PerturbationTheory.nb 1
Quantum Mechanics Perturbation Theory
Time-Independent Perturbation
◼ A Toy Model of Qubit
◼ General Ideas of Perturbation Theory
Perturbation theory: a set of approximation schemes that allows us to extend our knowledge about an exactly solvable quantum system to its vicinity (in the parameter space). Why do we need perturbation theory? Exact solutions are rare. ⇒ We have to rely on perturbation theory to go beyond them and make the most of these exact solutions. Separation of scales: physics often takes place at different energy scales, e.g. … → quarks (GeV) → nucleus (MeV) → atoms (eV) → molecules (100meV) → … ⇒ We can refine our descriptions by adding perturbative corrections progressively. What are the central problems in perturbation theory?