Can the Physics of Time Be Helpful in Solving the Differential Eigenequations Characteristic for the Quantum Theory? ()
ABSTRACT
The main differential equations of
quantum theory are the eigenequations based on the energy operator; they have
the energy as eigenvalues and the wave functions as eigenfunctions. A usual
complexity of these equations makes their accurate solutions accessible easily
only for very few physical cases. One of the methods giving the approximate
solutions is the Schrödinger perturbation theory in which both the energies and
wave functions of a more complicated eigenproblem are approached with the aid
of similar parameters characteristic for a less complicated eigenproblem. No
time parameter is necessary to be involved in these calculations. The present
paper shows that the Schrödinger perturbation method for non-degenerate
stationary quantum states, i.e. the
states being independent of time, can be substantially simplified by applying a
circular scale of time separately for each order of the perturbation theory.
The arrangement of the time points on the scale, combined with the points
contractions, gives almost immediately the series of terms necessary to express
the stationary perturbation energy of a given eigenproblem. The Schrödinger’s method is compared
with the Born-Heisenberg-Jordan perturbation
approach.
Share and Cite:
Olszewski, S. (2019) Can the Physics of Time Be Helpful in Solving the Differential Eigenequations Characteristic for the Quantum Theory?.
Advances in Pure Mathematics,
9, 228-241. doi:
10.4236/apm.2019.93011.