UDC 519.62; 530.145; 519.614 Model of Hydrogen Atom Quantum Measurements on Rigged Hilbert Spaces A. V. Zorin Peoples’ Friendship University of Russia 6, Miklukho–Maklaya str., Moscow, Russia, 117198 The measurement procedure makes the isolated (closed) quantum system to be the open one. <...> The author has proposed the method of establishing consistency between the theoretical data of conventional quantum mechanics of (isolated) quantum objects and experimental data on the measured values of the observables of corresponding open quantum objects. <...> In this paper, the proposed correspondence is used for the construction of rigged Hilbert spaces, in which the operators of measured the observables of hydrogen-like atom admit spectral decomposition. <...> Key words and phrases: operator of measured quantum observable, rigged Hilbert space, spectral decomposition of unbounded self-adjoint operator. 1. <...> The configuration space of an isolated physical object (for example, the Kepler According to the Weyl rule of quantization [4–7] quantum observables OW (A) are self-adjoint (unbounded) operators in rigged Hilbert space Φ ⊂ H = L2 (Q) ⊂ Φ∗. <...> The results of Shewell-Kuryshkin [8–10] on a one-to-one correspondence of quantization rules and quantum distribution functions (QDFs) puts the Weil rule into correspondence with Wigner QDF, so that ⟨A⟩ψ = (OW (A)ψ,ψ) = or, more generally, ⟨A⟩ρ = Tr (OW (A) ρ) = ∫ A(q, p)Wρ (q, p) dqdp. (2) In [11–13] on the basis of statistical correspondence, formulated by Blokhintsev and Terletsky, is developed the model of quantum mechanics with nonnegative QDF. <...> Kuryshkin quantization rule to each A(q, p) and some function φ ∈ H = L2 (Q) or density matrix ρ assigns the operator an explicit form of which is convenient to write with the help of auxiliary functions. <...> Classical observables A(q, p) are distributions on the phase space [1–3] of the object (system). <...> Zorin A. V. Model of Hydrogen Atom Quantum Measurements on Rigged . . . function on the phase space. <...> For pure state relations (6) and (7) retain the same form. <...> These formulations allowed [19] to prove that the operator of the measured observable Oρ (A) is given by the Weyl quantization rule for the ”measured” classical observable OW (Aρ), where Aρ (q, p) = (A∗Wρ) (q, p) and Wρ (q, p) are Wigner’s QDFs <...>