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Watson transform in quantum scattering.

Constantinos Valagiannopoulos1, Vassilios Kovanis2

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Summary
This summary is machine-generated.

This study enhances quantum particle scattering analysis by using the Watson transform for improved convergence. This method accurately models particle interactions in crystalline lattices, benefiting quantum research.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Nanotechnology

Background:

  • Canonical solutions for quantum particle wave functions in crystalline lattices with large nanoinclusions exhibit poor convergence.
  • The discrepancy arises because nanoinclusion size exceeds the matter wave wavelength.

Purpose of the Study:

  • To develop a more efficient method for analyzing high-energy quantum particle scattering by nanoinclusions.
  • To improve the convergence rate of wave function solutions in quantum scattering problems.

Main Methods:

  • Employing the Watson transform to reformulate wave function solutions.
  • Utilizing complex-ordered Hankel functions for enhanced series convergence.

Main Results:

  • The Watson transform provides an equivalent series representation with significantly improved convergence.
  • Demonstrated a versatile tool for rigorously solving particle interactions.

Conclusions:

  • The Watson transform is a powerful technique for overcoming convergence issues in quantum scattering.
  • This approach has broad applicability in quantum emission, interference, molecular fluctuations, and quantum signal processing.