Math Easy Solutions, use this: Electromagnetic potentials were introduced in classical electrodynamics as mathematical fields for describing electric and magnetic phenomena in a way that naturally satisfies part of Maxwell’s framework, but in quantum mechanics they can have direct physical significance rather than being just calculational tools (Wikipedia, MDPI). The Aharonov–Bohm effect is the key example, showing that the vector potential can influence a particle’s measurable quantum phase even in regions where the magnetic field is zero (Wikipedia, your post).