Model of Hydrogen Atom Quantum Measurements on Rigged Hilbert Spaces

The measurement procedure makes the isolated (closed) quantum system to be the open one. The operators of observables of rather simple explicit form are converted into pseudo-differential operators of more complex form. 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.

operator of measured quantum observable, rigged Hilbert space, spectral decomposition of unbounded self-adjoint operator