Magnetic-impurity states of electron in quantum well

A spectrum equation is obtained for the problem of determining the ground state of an electron in an attractive potential with a finite radius located in a quantum well situated in a perpendicular magnetic field H. The solution of this equation is expressed by the parameters of low-energy scattering at H=0. The expressions describing the diamagnetic and antidiamagnetic shifts from the quantum-dimensional spectrum boundary are found in the limiting cases of narrow and wide quantum wells. The criterion of electron state existence in an impurity potential located at an arbitrary distance from the center of a 2D structure is specified.