Question

When can I use semiclassical approximation?

Answer 1

I know that I can use semiclassical approximation for path integral approach (in quantum mechanics) ∫d[q]eiA∫d[q]eiA when action A>>1A>>1. But how shall I use such condition?
For example, assume that I have a particle with mass M in potential

V(q)=μ22q2−λ3q3V(q)=μ22q2−λ3q3. Then action A=∫dt(Mq˙22−μ22q2+λ3q3)A=∫dt(Mq˙22−μ22q2+λ3q3).

Suppose I want to determine μμ and λλ for which we can use semiclassical approximation. How to do this? I do not understand how to compare this action with 11.

Answer 2

Semiclassical physics, or simply semiclassical refers to a theory in which one part of a system is described quantum-mechanically whereas the other is treated classically. For example, external fields will be constant, or when changing will be classically described. In general, it incorporates a development in powers of Planck's constant, resulting in the classical physics of power 0, and the first nontrivial approximation to the power of (−1). In this case, there is a clear link between the quantum-mechanical system and the associated semi-classical and classical approximations, as it is similar in appearance to the transition from physical optics to geometric optics.