Physicist | Data Scientist | Researcher
My research in quantum foundations explores fundamental aspects of quantum mechanics, particularly focusing on representation freedom in the Dirac equation and its implications for scattering theory. This work reveals that seemingly equivalent mathematical formulations can lead to physically distinct predictions, challenging conventional assumptions about the uniqueness of quantum mechanical descriptions.
This work establishes a fundamental formulation of the Schrödinger equation, providing new perspectives on the foundations of non-relativistic quantum mechanics. The approach reveals connections between different formulations of quantum theory and suggests new avenues for understanding quantum phenomena.
View PaperInvestigates how the Dirac equation transitions to its non-relativistic form, providing rigorous analysis of the limiting procedure. This work is crucial for understanding how relativistic effects manifest in low-energy quantum systems and sets the stage for understanding representation freedom.
View PaperApplies the Lévy-Leblond equation to the hydrogen atom, demonstrating how alternative formulations can provide equivalent descriptions of atomic physics while offering different computational and conceptual advantages.
View PaperNote: The following impact analyses were generated by the AI model Claude based on research findings.
This groundbreaking paper demonstrates that transmission and reflection coefficients in Dirac equation scattering can depend on the choice of matrix representation, despite representations being related by unitary transformations. The work reveals spin-flip probabilities in scalar potentials that are absent in the standard Dirac representation, suggesting that representation choice has measurable physical consequences.
Key Finding: Quantum interference patterns emerge in scattering phenomena that depend on representation choice, providing testable experimental signatures and opening new avenues for understanding quantum mechanics.
View PaperThe discovery of representation-dependent scattering phenomena has profound implications across multiple areas of theoretical physics. Below are detailed explorations of how this work connects to and potentially impacts various fields: