How Practical Is Calculating Feynman Propagators for Quantum Oscillators?

[rishi]

I am pretty new to the subject and hope someone can give me certain links to start off.

We can express the time evolutions of a quantum mechanical state of a system as :
|psi(Xf,T)> = Gv(Xf,T;X0,0) |psi(X0,0)>

Now Gv can be expressed as a discretized Feynman Path integral which comes out to be a pretty complex integral (equation 4 in attached file). I am unable to understand as to how should I code a program to calulate this integral. any ideas!

 

[rick1138]

An excellent exposition of path integrals is available in Anthony Zee's book, Qyuantum Field Theory in a Nutshell.

 

[JohnDubYa]

I would suggest looking up Monte Carlo integration in a computational physics book, for example, Rubin Landau's or David Cook's.

 

[rishi]

some solution but...

I found an easy approach to calulate the Feynman propogator using Feynman path integral approach. Interested users can refer to paper titled:

"Three Methods for calculating the Feynman Propogator" by
F.A.Barone

However I now have one question. In this paper the feynman path was calulated using lagrangian for a quantum oscillator. Could anyone tell me how practical can this turn out to be. For e.g. can we make measurements of a state of a quantum oscillator. If we can then I think we should be able to use this approach to predict the output or make some sort of quantum gates. I haven't fully formalise if anything like this is possible. Maybe someone can tell me if this can be feasible at all or am I missing out some crucial point.

TIA