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.


hope this helps..

Answer 2

Usually, when doing approximations, one just solves it using them, and then look on the results when do they hold the assumptions you made. Like in perturbation theory, that you require the probability of change to be small.