TL;DR
This paper develops a path integral representation for elastic scattering amplitudes using the stationary Schrödinger equation, introduces methods for evaluating these integrals at large coupling constants, and compares results with exact solutions.
Contribution
It presents new methods based on uncertainty correlation for evaluating path integrals in elastic scattering at large coupling constants.
Findings
Calculated scattering lengths and cross sections for various potentials.
Compared approximate methods with exact results, showing good agreement.
Provided a framework for evaluating path integrals in quantum scattering problems.
Abstract
Representation of the elastic scattering amplitude in the form of the path integral is obtained using the stationary Schroedinger equation. A few methods of evaluation of path integrals for large coupling constants are formulated. The methods are based on the uncertainty correlation. The scattering lengths and cross sections are calculated for the right angled and singular potentials and the Yukawa potential. The comparison with exact results is made.
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