ABSTRACT
It is interesting to know when to expect the wave nature of a particle propagation to be well approximated by the properties of the trajectory of a classical particle. Usually, whenever there is an integral expression for a given quantity, it is often easier to employ approximate methods compared to a differential equation. It is simply a matter of convenience representing a path by a classical path and fluctuations around it. For the quasi-classical approximation, however, it is critical to expand around the path leading to the dominant contribution, i.e. the classical path. The knowledge of the stationary phase approximation is very appropriate to apply to path integration. This heading examines some specific systems of particular interest in people investigation. The harmonic oscillator has practical applications in a variety of domains of modern physics, such as molecular spectroscopy, solid state physics, nuclear structure, quantum field theory, quantum statistical mechanics and so on.
