Feed: Dr. Myron Evans
Posted on: Monday, November 22, 2010 11:20 AM
Author: metric345
Subject: R Spectra of the Hydrogen Atom
| The atomic spectrum of H is described excellently by sometime Oxford colleague Peter Atkins in the second edition of “Molecular Quantum Mechanics”. The energy levels that should be used in eq. (6) of note 165(1) are as follows (in units of ten power minus eighteen joules, see UFT 162, eq. (31)). They are all negative, because they are bound states of the atom. They are as follows;
E1 = -2.2; E2 = -0.55; E3 = -0.244; E4 = -0.1375; E5= -0.088; E6 = -0.061; E sub n = E1 / n squared. They are total relativistic energy in the limit when the Dirac equation becomes the Schroedinger equation. They are experimentally determined and there is no need to change them in any way. So the various R spectra can be calculated. The way in which Dirac reduces to Schroedinger is non-trivial and described by Ryder for example. The E of the Dirac equation is always the TOTAL relativistic energy, p is always the relativistic momentum. The Dirac equation of H gives features that the Schroedinger equation of H does not. For example, choose E1 and E2 and plot R against theta incremented from near zero to pi radians. Another is to choose E2 and E3 and repeat; another is to choose E3 and E4 and repeat. In all cases there is R sub + and R sub – . All the R spectra are different and completely new in concept. They turn the old physics into the new: a phoenix from the ashes type of happening.
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