On the magnetic Hooke-Newton transmutation of electrons

Abstract

The author investigates the Hooke-Newton transmutation of the electron in the uniform magnetic field. Two results are reported. First, the modulable quantum spectrum and spinor of the magnetic field are given. Spin exhibits its effect, even in the first order approximation of the power series expansion of the spectrum. Since the transmuted Coulomb interaction, attractive or repulsive, is determined by both the signatures of the charge and the total angular momentum, the pure spin states of different orientations experience the reverse Coulomb forces. This feature may be useful in grouping the pure spin states of the same orientation. Second, it is shown that the effect of the effective vector potential due to the geometry of conformal mapping can be generated by the vector potential of two fractional magnetic fluxes with the reverse directions which couple to the different components of the spinor. The equivalence shows the possibility of demonstrating the physics of the 2D electron in conformal space with an isotropic momentum modulation while interacting with the field of the magnetic fluxes.