We aim to describe the low-lying excited states in nuclei based on the time-dependent mean field theory. Quantum fluctuation is large in low-lying excitation energy region, such as shape coexistence. Some theoretical frameworks, such as generator coordinate method (GCM) and Bohr collective model, are often applied to describe the large amplitude collective motions. Here, we introduce a method which is called stationary phase approximation (SPA) to the path integral. Using SPA, we can obtain microscopic wave functions with good quantum number without any artificial assumption. In this presentation, I will explain the theoretical framework of SPA, and discuss a new method about the application of SPA in non-integrable systems. Also I will show some results about the advantage of SPA to describe the pairing collective motions.