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Can the Physics of Time Be Helpful in Solving the Differential Eigenequations Characteristic for the Quantum Theory?

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Document pages: 14 pages

Abstract: The main differential equations ofquantum theory are the eigenequations based on the energy operator; they havethe energy as eigenvalues and the wave functions as eigenfunctions. A usualcomplexity of these equations makes their accurate solutions accessible easilyonly for very few physical cases. One of the methods giving the approximatesolutions is the Schrödinger perturbation theory in which both the energies andwave functions of a more complicated eigenproblem are approached with the aidof similar parameters characteristic for a less complicated eigenproblem. Notime parameter is necessary to be involved in these calculations. The presentpaper shows that the Schrödinger perturbation method for non-degeneratestationary quantum states, i.e. thestates being independent of time, can be substantially simplified by applying acircular scale of time separately for each order of the perturbation theory.The arrangement of the time points on the scale, combined with the pointscontractions, gives almost immediately the series of terms necessary to expressthe stationary perturbation energy of a given eigenproblem. The Schrödinger’s method is comparedwith the Born-Heisenberg-Jordan perturbationapproach.

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