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On the basis of analytic solutions of Schrodinger and Pauli equations for auniform magnetic field and a single attractive $\delta({\bf r})$-potential theequations for the bound one-active electron states are discussed. It is varyimportant that ground electron states in the magnetic field essentiallydifferent from the analog state of spin-0 particles that binding energy hasbeen intensively studied at more then forty years ago. We show that bindingenergy equations for spin-1/2 particles can be obtained without using of awell-known language of boundary conditions in the model of $\delta$-potentialthat has been developed in pioneering works. Obtained equations are used forthe analytically calculation of the energy level displacements, whichdemonstrate nonlinear dependencies on field intensities. It is shown that in acase of the weak intensity a magnetic field indeed plays a stabilizing role inconsidering systems. However the strong magnetic field shows the oppositeaction. We are expected that these properties can be of importance for realquantum mechanical fermionic systems in two- and three-dimensional cases.Comment: 18 page

Scalar and spinor particles with low binding energy in a strong stationary magnetic field in two and three dimensions