Quantized planary dynamics in orthogonal magneto-electrostatic fields

At the first quantization level, we deal with the planary dynamics of a charged scalar evolving in static orthogonal magnetic and electric fields. Working in a relativistic approach, we get the quantum eigenstates and the energy spectrum exhibiting a non-linear dependence on the exterior fields and the particle momentum parameter. Analyzing the generalized Landau-type energy levels, we point out a shift of the Larmor pulsation, due to the electrostatic field and derive a critical induction-energy spectrum. The same has been done for strong magnetic fields and a compulsory relation between the particle momentum and the electric field intensity has been obtained. For quasi-on-shell particles, moving in either strong or weak magnetic field, we derive the completely possible momentum spectrum. It turns out that, in extremely faint electrostatic fields, it yields the same momentum quantization.