By obtaining pin, like a tiny string, as a further intrinsic quantum property with the general nature of an intrinsic linear momentum of an observable quantum state besides spin as an intrinsic quantum property with the general nature of an intrinsic angular momentum of an observable quantum state, we would find the subatomic particles contain spin, pin, magnetic moment and electric moment, the four intrinsic quantum properties of their own. As such, considering the four intrinsic quantum properties of subatomic particles and remembering the Maxwell’s realization that the laws governing electricity and magnetism are identical, we would be able to obtain theoretically the isolated electric monopoles as free quantized electric charges carried by some particles, as well as, the isolated magnetic monopoles as free quantized magnetic charges carried by some specific particles in quantum mechanics and particle physics. As such, we would obtain the Gauss’s law and the Coulomb’s law in magnetostatics analogous to the same laws in electrostatics, and also magnetic charge density and magnetic current density coun-terpart of electric charge density and electric current density with respect to free quantized magnetic charge. We would then get the modified Maxwell’s equations as duality symmetry and the modified Lorentz force law considering both electric and magnetic charges, where the electric and magnetic parameters are being invariant under the duality transformation exchanges in all respect.