New to Feynman Path Integral

In summary, the conversation discusses the use of Feynman path integrals to express the time evolution of a quantum mechanical state and the complexity of calculating this integral. It is recommended to refer to Anthony Zee's book, Quantum Field Theory in a Nutshell, for a better understanding. Other suggestions include looking up Monte Carlo integration in computational physics books and reading F.A. Barone's paper on calculating the Feynman propagator. The question of using this approach for practical purposes, such as making measurements or predicting outputs using quantum gates, is also raised. It is unclear if this is feasible and further research is needed.
  • #1
rishi
3
0
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!
 

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  • #2
An excellent exposition of path integrals is available in Anthony Zee's book, Qyuantum Field Theory in a Nutshell.
 
  • #3
I would suggest looking up Monte Carlo integration in a computational physics book, for example, Rubin Landau's or David Cook's.
 
  • #4
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
 

1. What is the Feynman Path Integral?

The Feynman Path Integral, also known as the Feynman-Kac formula, is a mathematical tool used in quantum mechanics to calculate probabilities of particle interactions. It is based on the idea that a particle can take multiple paths to reach a certain point, and the total probability is the sum of all possible paths.

2. How is the Feynman Path Integral different from other quantum mechanical approaches?

The Feynman Path Integral is a different approach to calculating quantum mechanical probabilities compared to the traditional Schrödinger equation. It takes into account all possible paths that a particle can take, rather than just the most probable path. This allows for a more accurate representation of quantum systems.

3. What is the significance of the "New" in "New to Feynman Path Integral"?

The "New" refers to the recent development and advancements in the application of the Feynman Path Integral. It is a relatively new concept in the field of quantum mechanics and has gained more attention and interest in recent years.

4. How is the Feynman Path Integral used in practical applications?

The Feynman Path Integral is used in various practical applications, such as in calculating the behavior of particles in a magnetic field or predicting the properties of complex molecules. It is also used in theoretical physics to study quantum field theories and in cosmology to understand the behavior of the universe at a quantum level.

5. Is the Feynman Path Integral a difficult concept to understand?

The concept of the Feynman Path Integral may be challenging to grasp at first, but with proper understanding of quantum mechanics and mathematical techniques, it can be comprehended. It is a fundamental concept in quantum mechanics and is used by many scientists and researchers in their work.

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