ABSTRACT
Synopsis: It is rare that exact solutions for physical quantum systems are available, and likely that one or more types of perturbation theories need to be applied. Three time-independent, or static, methods are discussed. Using exact energy shift formulas, a result correct to second order for the perturbed system energy is derived and applied to a two-state system and a harmonic oscillator example. The WKB semiclassical approximation is motivated, and applications to barrier penetration and various types of bound-state problems are made. The third class of methods gives upper limit estimates of system ground-state properties based on energy functional variations.
