Sakurai's treatment of Feynman's Path Integral

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Discussion Overview

The discussion revolves around Sakurai's treatment of Feynman's path integral, focusing on the understanding and applications of the propagator derived from it. Participants express their confusion and seek additional resources for better comprehension of the topic, which encompasses theoretical aspects of quantum mechanics and path integrals.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant expresses confusion about the purpose of the propagator and seeks alternative sources for the path integral derivation.
  • Another participant explains that the propagator provides a complete solution to the Schrödinger equation for arbitrary initial conditions and encodes information about bound states and their energies.
  • A suggestion is made to refer directly to Feynman's own writings for a clearer understanding of the physical concepts behind the mathematics.
  • Recommendations for additional resources include a book by Schulman on path integrals and a book by Ramond on quantum field theory, highlighting the utility of path integral methods in gauge field theory.
  • A participant mentions Cohen-Tannoudji's axiomatic treatment of path integrals as a valuable resource in quantum mechanics.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best resource for understanding the path integral; multiple competing views and recommendations for literature are presented.

Contextual Notes

Some participants express uncertainty regarding the clarity of Sakurai's treatment, indicating that further reading and problem-solving may be necessary to grasp the concepts fully.

Who May Find This Useful

This discussion may be useful for students and researchers interested in quantum mechanics, particularly those seeking to understand Feynman's path integral and its applications in quantum field theory.

mattlorig
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I just finished reading Sakurai's treatment of feynman's path integral, and I'm left feeling really stupid. So the integral gives the propagator, which represents a transition amplitude. I'm left wondering what we use that for. Perhaps I'll understand when I start working some problems, or perhaps after I read the derivation a few more times. But, just to cover my bases, can anybody recommend a different source of the path integral derivation (which, according to sakurai really isn't a derivation)?
 
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The propagator is good for a lot of things. It gives you a complete solution to the Schrödinger equation for arbitrary initial conditions so that if K(x,t;x',t') is the propagator then

\psi(x,t) = \int dx' \, K(x,t;x',0) \psi(x',0)

and \psi(x,t) satisfies the Schrödinger equation. It can do a lot more too, it encodes all the information about the bound states and their energies.

Sakurai's treatment is rather terse. A great source for path integrals in general is "Techniques and Applications of Path Integration" by Schulman. A good online source is http://arxiv.org/abs/quant-ph/0004090
 
mattlorig said:
I just finished reading Sakurai's treatment of feynman's path integral, and I'm left feeling really stupid. ... can anybody recommend a different source of the path integral derivation (which, according to sakurai really isn't a derivation)?

Go straight to the source, Feynman himself! He is justly well-known for providing good physical pictures behind the math. See the thread "I need some bibliography" for some of his writings ...

David
 
I recommend the book by Ramond "Quantum field theory, a modern primer"
Path integral methods is a powerful tool in Quantum field theory,
particularly in Gauge field theory.
 
I also like Cohen-Tannoudji's axiomatical treatmeant of path-integrals. In the first volume of his QM book.

Daniel.
 

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