Abstract
It is the purpose of this paper to investigate the behavior of a charged transformation-wave in a uniform magnetic field. We first derive the equation which a transformation-wave needs to satisfy, and then, as the main application, the magnetic duality of the Hooke-Newton transmutation is performed by a conformal mapping which generates the novel states with the following characteristics: (a) bound or scattering states are classified by the signatures of the quantum number of the angular momentum and the charge of the particle; (b) the angular momentum satisfies the half-integer quantization rule; and (c) the mass parameter to reach the states is isotropic. Finally, as an alternative application, we report the construction of the fractional angular momentum and fractional Landau levels with the transformation design method.
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