May 18th, 2020

лошадь, диаграмма, Фейнман

О распаде связанного мюона

Очень симпатичный расчетик:)

Decay of a bound muon into a bound electron: https://arxiv.org/abs/2005.07276

When a muon bound in an atom decays, there is a small probability that the daughter electron remains bound. That probability is evaluated. Surprisingly, a significant part of the rate is contributed by the negative energy component of the wave function, neglected in a previous study. A simple integral representation of the rate is presented. In the limit of close muon and electron masses, an analytic formula is derived.
лошадь, диаграмма, Фейнман

Рассеяние пакета на одномерной яме с помощью интегралов по траекториям в реальном времени

Вряд ли буду вникать, но пусть полежит.

Scattering using real-time path integrals: https://arxiv.org/abs/1712.00046
W. N. Polyzou, Ekaterina Nathanson
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.
Comments: 26 pages, 35 figures (revised )