The behavior of atomic H in a semi-bounded space z ≥ 0 with the condition of "not going through" the boundary (the surface z = 0) for the electronic wavefunction (WF) is considered. It is shown that in a wide range of "not going through" condition parameters the effective atomic potential, treated as a function of the distance h from H to the boundary plane, reveals a well pronounced minimum at certain finite but nonzero h, which describes the mode of "soaring" of the atom above the plane. In particular cases of Dirichlet and Neumann conditions, the analysis of the soaring effect is based on the exact analytical solutions of the problem in terms of generalized spheroidal Coulomb functions. For h varying between the regions h ) a B and h ( a B , both the deformation of the electronic WF and the atomic state are studied in detail. For a more general case of Robin (third type) condition, the variational estimates and direct numerical tools are used. By means of the latter it is also shown that in the case of a sufficiently large positive affinity of the atom to the boundary plane a significant reconstruction of the lowest levels takes place, including the change of both the asymptotics and the general dependence on h. K E Y W O R D S confined quantum systems, levels reconstruction, soaring effect 1 | INTRODUCTIONConsiderable amount of theoretical and experimental activity has been focused recently on spatially confined atoms and molecules. [1][2][3] The interest is largely due to the nontrivial physical and chemical properties that arise for quantum systems in such a state of complete or incomplete confinement. The interaction of confined particles with the environment, forming the cavity or volume boundary, is usually simulated by means of a suitable boundary condition, imposed on their wavefunctions (WF). The pioneering works on quantum system in a closed cavity are the Wigner-Seitz model [4,5] and the papers [6,7] on atomic H in a spherical cavity. More concretely, in the Wigner-Seitz model the metallic bond formation in alkali metals has been considered in terms of the Neumann condition for the valence electron on the boundary of the corresponding Wigner-Seitz cell. In Ref.[6] the exact solution for atomic H in a spherical cavity with the Dirichlet boundary condition was found, while in Ref.[7] such a model has been used for description of atomic H under high pressure.Atoms in the Euclidean half-space ℜ 3 / 2 have been first explored by Levine, [8] devoted to the properties of the impurity donor atom placed on the plane boundary of the dielectric crystal. Due to a large positive affinity it is energetically favorable for the valence electron to reside inside the crystal that allows to simulate the crystal boundary by means of the Dirichlet condition imposed on the electronic WF. Afterwards, this model All authors contributed equally to this work.

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