We discuss the equations for the bound one-active electron states based on the analytic solutions of the Schrodinger and Pauli equations for a uniform magnetic field and a single attractive δ(r)-potential. We show that the magnetic field indeed plays a stabilizing role in considered systems in a case of the weak intensity, but the opposite occurs in the case of strong intensity. These properties may be important for real quantum mechanical fermionic systems in two and three dimensions. In addition, we obtained that including the spin in the framework of the nonrelativistic approach allows correctly taking the effect of the magnetic field on the electric current into account.

The magnetic field plays a stabilizing role in bound electron states with weak intensity, but the opposite effect at strong intensity, potentially impacting quantum mechanical fermionic systems in two and three dimensions.

Physics of Particles and Nuclei

The energy level shifts, wave functions and the probability current distributions for the bound scalar and spinor particles moving in a uniform magnetic field

The energy level shifts, wave functions and the probability current distributions for the bound scalar and spinor particles moving in a uniform magnetic field

Key Takeaway: The magnetic field plays a stabilizing role in bound electron states with weak intensity, but the opposite effect at strong intensity, potentially impacting quantum mechanical fermionic systems in two and three dimensions.