Is the Rydberg–Ritz Relationship Valid?

Abstract

In the first part of this chapter, it is shown that the linear relationship between the energy E _n of any quantum state of the hydrogen atom and the negative inverse square of the quantum numbern can be used, together with the Rydberg–Ritz combination principle, to provide an internal check of its own validity, utilizing the most accurate atomic spectral data. This internal check uses the fact that the value of the linear proportionality constant can be obtained both from the slope and from the intercept of the straight line on the energy axis. If these two values differ by more than that allowed by experimental scatter, there is serious doubt about the validity of the inverse-squared relationship. This analysis shows that the relationship is nearly but not exactly satisfied. In the second part of this chapter, it is shown that the usual interpretation of the inverse-squared relationship obscures the fact that it actually leads to imaginary values for the quantum numbers and not to the real integral values as assumed up to now. Both analyses indicate that nonrelativistic quantum mechanics is not based upon solid foundations as assumed up till now, and requires critical reexamination, especially with respect to the role of time.