Abstract

Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While imaginary time treatments of scattering are possible, imaginary time is not a natural framework for treating scattering problems. Purpose: To test a recently introduced method for performing direct calculations of scattering observables using real-time path integrals. Methods: The computations are based on a new interpretation of the path integral as the expectation value of a potential functional on a space of continuous paths with respect to a complex probability distribution. The method has the advantage that it can be applied to arbitrary short-range potentials. Results: The new method is tested by applying it to calculate half-shell sharp-momentum transition matrix elements for one-dimensional potential scattering. The calculations for half shell transition operator matrix elements are in agreement with a numerical solution of the Lippmann-Schwinger equation. The computational method has a straightforward generalization to more complicated systems.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.