Hi, I have been looking for rigorous mathematical conditions for when the WKB approximation may be applied. Here is my understanding of the topic. We start with the most general form that the wavefunction could take, i.e. exp[if(x)/h] , Where "i" stands for square root of -1, f(x) is some real function of x, h stands for "h bar",that is the original Planck's constant divide by 2pi. Any complex function of x can be written this way. Now we express f(x) as a series in powers of "h bar", i.e. f(x) = f0 + hf1 + h2f2 + ... Where again "h" actually stands for "h bar" . We now put this wave function into schrodinger's one dimensional equation to find various relations. Now in this entire process, here comes the WKB "approximation" , the approximation being, to neglect h2 dependant and all higher terms in the expansion of f(x) i.e. to take f(x) to be f(x) = f0 + hf1 My question: when can we do so ? That is, mathematically, when can we ignore h2 and higher order terms ?