Sakurai's treatment of Feynman's Path Integral

[mattlorig]

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)?

 

[Physics Monkey]

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

 

[straycat]

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

 

[snooper007]

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.

 

[dextercioby]

I also like Cohen-Tannoudji's axiomatical treatmeant of path-integrals. In the first volume of his QM book.

Daniel.