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## Интегральное представление собственных состояний 3:(-1) резонансной наноловушки Пеннинга

О.В. Благодырева, М.В. Карасев, Е.М. Новикова

We discuss physical parameters of quantum Penning nanotraps. In the case of 3:(-1) resonance between transverse frequencies of the trap we describe the reproducing measure on symplectic leaves corresponding to irreducible representations of non-Lie symmetry algebra with qubic commutation relations. Nonhomogeneity of the magnetic field and anharmonicity of the electric potential of the trap, after double averaging, generate an effective Hamiltonian which becomes a second order ordinary differential operator in the irreducible representation. We obtain an integral formula for asymptotical eigenstates of the perturbed 3:(-1) resonance Penning trap via the eigenfunctions of this operator, as well via the coherent states and the reproducing measure.