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 PaperWe show that nilpotent matrices that yield the Schrodinger equation from its first order form encode the fingerprints of grand unified theories. We perform a rigorous search for all such nilpotent matrices and find that the resulting matrices naturally organize into suggestive group theoretic structures without any other a priori assumptions. The antisymmetric sector consists of three groups of sixteen matrices, each of which further splits as 16 = 12 + 4 and exhibits unique characteristics in the step potential scattering problem. The symmetric zero-diagonal sector also forms three families, mirroring the quark-lepton decomposition of the Pati-Salam model. These results may help answer why there are three families of fermions and also demonstrate that the 4 x 4 matrix algebra is a compact, nontrivial shadow of the SO(10) embedding, with fermion-like and gauge-like subspaces.
View PaperThis 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.
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: