Semi-classical Approximation: WKB Method
摘要
In this chapter WKB approximation, which is semi-classical and valid when potential is a slowly varying function of position, is presented for solving Schrödinger equation. This approximation breaks down near CTPs and connection between two WKB solutions on either side of CTP is made by connection formulas, obtained by matching the two solutions with solutions near CTP, assuming a linear potential approximation. It gives a simple energy quantization relation for bound states and transmission coefficient through a barrier. Some basic properties arising from the energy equation are also discussed. Applications to simple harmonic oscillator and alpha-decay are discussed.