Research

Projects I have been working on

Mainly focused on non-relativistic quantum mechanics and its applications in condensed matter physics. But seeking to engage in other topics like gravitation

Abstract representation of entangled electron pairs

From Schrödinger to Dirac: Gauge Invariance, Landau Quantization, and Probability Currents — Minimal Coupling, Gauge Invariance & Landau Levels

How EM fields enter quantum dynamics: canonical → minimal coupling, U(1) gauge transformations, and spectra in uniform fields.

Galaxy cluster illustrating gravitational lensing

Symmetries of the Pauli Equation: Noether Currents and Conservation Laws — Spin SU(2), Magnetic Interactions & Conserved Quantities

Spin rotations, Space-time traslations, generators/commutators and constants of motion in the Pauli Hamiltonian. (Soon)

Computer simulation of neutrino oscillations

Spin Currents in the Pauli Equation: Applications to the Quantum Hall Regime — Continuity Equation, Spin Torque & Physical Interpretation

Spin‑current continuity, torque terms and working definitions in condensed‑matter contexts. (Available soon)