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Watson transform in quantum scattering
Constantinos Valagiannopoulos1, Vassilios Kovanis2
1School of Electrical & Computer Engineering, National Technical University of Athens, Athens, 15772, Greece. valagiannopoulos@ece.ntua.gr.
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.
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.
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