Path integral formulation of non-relativistic quantum mechanics

In summary, the path integral formulation is a mathematical framework used to describe the behavior of quantum systems. It involves summing over all possible paths that a particle can take in order to calculate the probability of different outcomes. This approach differs from other formulations of quantum mechanics, such as the Schrödinger equation, as it is based on a probabilistic approach and allows for the incorporation of time-dependent potentials and relativistic effects. The path integral formulation is significant in quantum mechanics as it provides a powerful tool for calculating complex systems and helps bridge the gap between classical and quantum mechanics. However, it also presents challenges, such as the need to sum over an infinite number of paths and the difficulty in interpreting these paths. The path integral formulation has practical
  • #1
go quantum!
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I am looking for a textbook that introduces and discusses the path integral formulation of non-relativistic quantum mechanics? Would you have some suggestions for me? Thanks.
 
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  • #2
My advice is to look for Feynman and Hibbs' book of 1965. Normally many books on QM have a special chapter on the path integral formulation anyways, but perhaps you won't find such discussions as enough.
 
  • #3

What is the path integral formulation of non-relativistic quantum mechanics?

The path integral formulation is a mathematical framework for describing the behavior of quantum systems. It involves summing over all possible paths that a particle can take in order to calculate the probability of different outcomes.

How is the path integral formulation different from other formulations of quantum mechanics?

The path integral formulation is based on a probabilistic approach, rather than the wave function approach used in the Schrödinger equation. It also allows for the incorporation of time-dependent potentials and can be extended to include relativistic effects.

What is the significance of the path integral formulation in quantum mechanics?

The path integral formulation provides a powerful tool for calculating the behavior of quantum systems, especially in complex situations where other methods may be difficult to apply. It also helps to bridge the gap between classical and quantum mechanics.

What are the main challenges in using the path integral formulation?

One of the main challenges is the requirement to sum over an infinite number of possible paths, which can be computationally intensive. Additionally, the interpretation of the path integral can be difficult, as it involves considering all possible paths, including those that may seem physically impossible.

How is the path integral formulation used in practical applications?

The path integral formulation has been used in a wide range of applications, including quantum field theory, condensed matter physics, and quantum information theory. It has also been applied to problems in finance, biology, and other fields where probabilistic calculations are needed to describe complex systems.

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