The harmonic oscillator in terms of path integrals without dirac notation

[roberto85]

Hi, I'm desperately searching for some literature which discusses the harmonic oscillator, preferably simple, in terms of the path integral formulation. I am unfamiliar with dirac notation and want something as simple as possible which gives general results of the harmonic oscillator in terms of path integrals. Also avoiding schroedinger or matrix algebra also in the literature for this particular piece I am writing, pure PI formulation is required. Also, internet sources would be easiest.

I have tried a few books, sakurai, feynman and hibbs and a few others but not found what I am looking for. Please if anyone can help me, I am on a deadline. Many thanks

Roberto

 

[Dyson]

Hi,maybe i can help you.
The book named <<Feynman's thesis--a new approach to quantum mechanics>> may be of great use to you!
Write me an email so that i can give you a reply and send you the book.
My email is zhaoliang_fly@yahoo.com.cn

 

[Entropia]

,

There are several resources available online that discuss the harmonic oscillator in terms of path integrals without using Dirac notation. One possible source is the blog "Quantum Field Theory for the Gifted Amateur" by Tom Banks, which has a section on the harmonic oscillator in path integral form. Another possible resource is the paper "Quantum mechanics in path integral form: The harmonic oscillator" by Charles S. Peskin, which can be found on the arXiv preprint server. Additionally, you may find helpful information on the website "Path Integrals in Quantum Mechanics" by Professor Holger Bech Nielsen from the University of Copenhagen.

In general, the path integral formulation of the harmonic oscillator involves integrating over all possible paths that the system could take in time, weighted by a phase factor. This allows for a more intuitive understanding of the system compared to traditional Schrodinger or matrix algebra approaches. The resulting path integral can be solved using various techniques, such as the saddle point approximation or perturbation theory.

I hope these resources will be helpful in your research. Good luck with your project!