The problem of creating pure and entangled states for the optical implementation of quantum computations, as well as a number of tasks involving the formation of active media on quantum dots, requires the formulation of conditions under which they contain exactly one bound energy level. The critical conditions are studied for the appearance of the first bound single-electron state, localized on a spherical quantum dot of small size in an external magnetic field. A simple analytical representation is obtained for the wave function of such a state, and the equation for determining its binding energy is formulated and solved. The results are compared with the well-known delta-potential approximation. It is shown that a bound level appears in an empty quantum dot only when the magnetic field exceeds a definite threshold value.
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