This talk has two parts. In the first part I will explain that the Differential Galois theory is the tool that explains why it Is possible to obtain closed form solutions for the WKB approximation of integrable Hamiltonian systems in quantum mechanics and the many open problems motivating this remark. The second part will be devoted to one of these problems: the Schwarzschild black-hole, this a joint work in progress with Álvaro Pérez-Raposo.