Magnetic Orbitals - The First Visual Revelation of Quantum Geometries in the Macroscopic World

First publication: 15 July 2025

This research introduces an experimental methodology capable of revealing geometrical structures corresponding to spherical harmonics within macroscopic magnetic fields, making visible field configurations never previously observed experimentally in the real world.

Atomic orbitals are well known geometrical structures emerging from quantum mechanics. They arise as solutions of the Schrödinger equation for the hydrogen atom and are mathematically described by spherical harmonics. In modern physics these forms are typically interpreted as probability distributions associated with the electron’s quantum state rather than as spatial geometries observable at the macroscopic scale.

This work presents, for the first time, a three-dimensional experimental visualization of structures isomorphic to atomic orbitals, obtained by detecting and spatially mapping magnetic field configurations using Hall-effect sensors.

The method employs a bipolar Hall sensor operating in dynamic scanning mode while maintaining a constant angular orientation relative to the magnetic source. This configuration differs from conventional magnetic field visualizations derived directly from Maxwell’s equations.

When the field is explored considering dipole-dipole interactions and maintaining a fixed sensor orientation during spatial scanning, the measurements correspond to local projections of the magnetic field along a constant angular direction. Reconstructing these projections reveals three-dimensional structures that closely correspond to the spherical harmonic geometries associated with hydrogen atomic orbitals.

Such configurations do not normally appear in standard magnetic field representations because their emergence depends on a measurement geometry that highlights the angular components of dipolar interactions.

From this observation derives the title of the research.

The observed structures coincide with forms historically associated with the quantum solutions of the Schrödinger equation for hydrogen, yet here they appear as measurable geometrical configurations of a macroscopic magnetic field, suggesting a structural relationship between these two descriptions.

The research also provides interpretations consistent with both classical mechanics and quantum mechanics, offering complementary perspectives. Using the classical geometry of magnetic fields as a framework, several quantum concepts acquire an intuitive geometric interpretation.

The work also includes a replicable experimental method for generating and visualizing these structures by scanning one or more permanent magnets with Hall sensors, effectively providing a form of three-dimensional magnetic tomography ("Magnetic CT Scan").

Official DOI: https://doi.org/10.5281/zenodo.15936280

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