Topic: An Alternative Method to WKB Approximations and Its Applications to Quantum Mechanics, Cosmology and Gravitational Wave Physics 

Speaker:  Prof. Anzhong Wang

Coordinates: Classroom 2106, 16:00, Friday, June 30

Abstract: The WKB method plays an essential role in the development of quantum mechanics (QM). However, it is valid only when certain conditions hold. In the past couple of years, we have systematically developed a new method, the uniform asymptotic approximation, which is applicable to all kinds of the second-order linear differential equations, and in which the upper bound of errors is known explicitly at each order of approximations and can be as smaller as 0.15% up to the third-order approximation. Applying it to several well-known cases in QM, we find that significant improvement over the WKB method can be achieved. In this talk, I shall first present a detailed description of the method and then show how to apply it to study gravitational waves propagating in the curved universe and cosmological perturbations after quantum gravitational effects are taken into account.