# Discussion of Note 330(7)

These results are the first time that the Dirac equation has been developed without using his rough approximation, and they can be compared directly with spectral data. They are worked out in the first approximation with the non relativistic H wavefunctions, which for H is a good approximation. I will correct the errata shortly. Section 3 has already been posted as mentioned by Horst and contains a comparison of expectation values of 1 / r cubed and 1 / r fourth and a computation of the new terms. At present I am working on UFT331 and a new type of relativistic Zeeman spectroscopy. All these results are being recorded and could be tested experimentally at an AIAS institute at Aberystwyth, and also of course elsewhere. This method can also be developed extensively with computational quantum chemistry code libraries around the world, for example IBM MOTECC for which I was the lead writer at IBM Kingston, New York State, in 1988. Well developed code for the Dirac equation can be modified, producing many new spectral patterns of immediate use to analytical and pathological laboratories for example, using Fourier transform IR, ESR and NMR, and also MRI.

To: EMyrone@aol.com
Sent: 28/10/2015 13:50:41 GMT Standard Time
Subj: PS: Re: Discussion of Note 330(7)

Attachment was missing 🙂

Am 28.10.2015 um 14:49 schrieb Horst Eckardt:

I computed <U> and <Hso2> by Maxima, see last two formulas in the protocol. In <U> (eq.29) some factors are wrong, probably the Bohr radius (%o8) was not correctly inserted. in (30) a factor c^2 is superflous and m squared reduces to m.

Horst

Am 28.10.2015 um 09:58 schrieb EMyrone:

Many thanks for going through this. The dimensionality of Eq. (30) appears to be correct. The term in brackets is energy and when divided by m c squared is dimensionless. So the term becomes the usual gyromagnetic ratio (e h bar / (2m)) multiplied by sigma dot B multiplied by a dimensionless constant. This can be run through Maxima to double check. Very many new ESR, NMR, MRI and Zeeman and anomalous Z|eeman spectroscopies emerge – again by scholarly scrutiny of the ninety year old basics. I think that there will also be a whole pile of new results in nonlinear optics and quantum optics. Something for the younger generations to think about. In ECE two all this theory is related to torsion and curvature and spin connection.

To: Emyrone
Sent: 27/10/2015 19:45:50 GMT Standard Time
Subj: note 330(7)

How did you get the constants in eq.(30)? Eq. (28) is

< 1/r > = 1 / (n^2*a0)

with Bohr radius a0. Inserting this into (27) gives (30) but with m
instead of m squared. I do not know if (29) is correct.

Horst

330(7).pdf