Version 1
: Received: 29 March 2024 / Approved: 29 March 2024 / Online: 29 March 2024 (13:55:05 CET)
How to cite:
Durmagambetov, A. Coordinate Transformations and Phase Sensitivity in the Schrödinger Equation: Unraveling Fundamental Properties. Preprints2024, 2024031828. https://doi.org/10.20944/preprints202403.1828.v1
Durmagambetov, A. Coordinate Transformations and Phase Sensitivity in the Schrödinger Equation: Unraveling Fundamental Properties. Preprints 2024, 2024031828. https://doi.org/10.20944/preprints202403.1828.v1
Durmagambetov, A. Coordinate Transformations and Phase Sensitivity in the Schrödinger Equation: Unraveling Fundamental Properties. Preprints2024, 2024031828. https://doi.org/10.20944/preprints202403.1828.v1
APA Style
Durmagambetov, A. (2024). Coordinate Transformations and Phase Sensitivity in the Schrödinger Equation: Unraveling Fundamental Properties. Preprints. https://doi.org/10.20944/preprints202403.1828.v1
Chicago/Turabian Style
Durmagambetov, A. 2024 "Coordinate Transformations and Phase Sensitivity in the Schrödinger Equation: Unraveling Fundamental Properties" Preprints. https://doi.org/10.20944/preprints202403.1828.v1
Abstract
This study delves into the Schrödinger equation's new invariants, shedding light on their crucial implications for theoretical physics and beyond. Specifically, it explores the behavior of scattering amplitudes and bound states concerning the choice of coordinate systems. The research unveils that while the energy of bound states remains invariant under coordinate transformations, the phase of scattering amplitudes undergoes variations, underscoring its pivotal role in theories reliant on phase normalization. Moreover, these findings have played a pivotal role in constructing estimates for three-dimensional Navier-Stokes equations, enhancing our ability to model complex fluid dynamics with greater precision and reliability. Additionally, in seismic exploration, tomography, and ultrasound imaging, these properties allow researchers to optimize phase selection, facilitating the most effective interpretation of measurement results. This strategic phase manipulation ensures clearer insights into subsurface structures, tissue composition, and fluid dynamics, with the flexibility to seamlessly transition back to the original coordinate system post-interpretation. This interdisciplinary synergy underscores the profound impact of fundamental theoretical research on advancing practical applications across diverse scientific domains.
Keywords
Schrödinger equation; inverse; amplitudes
Subject
Physical Sciences, Fluids and Plasmas Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
