Many thanks again! Agreed about eqs. (7) and (12). To be accurate of course Eq. (26) has to be solved numerically or analytically to find the effect on the energy levels of H and to detect splitting of spectral lines, if any, due to ubiquitous Thomas precession. There is an extra L squared operator:
L squared psi = l(l+1) h bar squared psi
and this may well lead to spectral splitting. As you infer this is an interesting effect.
To: EMyrone@aol.com
Sent: 29/07/2014 15:27:45 GMT Daylight Time
Subj: Re: 267(5): Effect of Ubiquitous Thomas Precession on the Schroedinger EquationIt seems that eq.(7) should read
MG –> k/m = hbar c alpha_f / m
but (11) is correct.
EQ. (25) seems to define a correction to the angular momentum. This appears at the LHS when the delta operator is rewritten to spherical coordinates. I am not sure if this results in a simple correction x^2 L^2 ananlogues to x^2 k.Horst
EMyrone@aol.com hat am 29. Juli 2014 um 11:51 geschrieben:
This note shows that the effect is to make the ellipse of note 267(4) precess, with precession factor given by Eq. (11). The Schroedinger equation is changed to Eq. (26), which appears to be insoluble analytically but can be approximated by Eq. (38) which gives Schroedinger solutions with k replaced by x squared k wherever k occurs in the wavefunctions (k = e squared / (4 pi eps0)), so e squared can be coded in as x squared e squared. The precession factor x is very close to unity as in planetary precession, but spectral techniques are very precise and might be able to observe its effects. The expectation values are defined in Eq. (40) and have to be worked out nmerically as in Note 267(4). The ubiquitous Thomas precession changes the entire subject of computational quantum chemistry. It is caused by a rotating Minkowski metric. The rotation in this case is that of the electron around the proton in an H atom. In planetary precession it is the rotation of m around M. In pendulum precession it is the rotation of the earth’s surface. It is not the Thomas factor of a half, which is already factored in to the fermion equation, it is ubiquitous, and appears for example in pendulum precessions, planetary orbits and now it has been realized to exist in atomic and molecular spectra. As usual this is a simple first theory that can be greatly refined.