Discussion of 326(4)

Thanks again for going through 326(4). Agreed with the first two points, I thing that the factor 2 is alright because 1 + gamma is approximately 1 + 1 – v squared / (2 c squared).

To: EMyrone@aol.com
Sent: 29/08/2015 11:20:02 GMT Daylight Time
Subj: Re: 326(2): Quantization of the Sommerfeld Hamiltonian

In eq.(39) it should read at the RHS:

hbar^2 / 2 m^2 c^2

(with m squared). In eq.(46) the factor E seems to be missing. Should there be a “3” instead of “2” because of 1+gamma in eq. (30)?

Horst

Am 24.08.2015 um 15:57 schrieb EMyrone:

This note uses a Dirac type quantization to produce the equation (21), a relativistic Schroedinger equation which must be solved for the wavefunctions psi. In general this is a highly non trivial procedure which must be carried out numerically in three dimensions. However, it is straightforward to show that this type of quantization produces small shifts in the H atom energy levels given by the expectation value (28). The Thomas factor is given correctly by the Sommerfeld atom, but there is no spin orbit interaction, because the Sommerfeld atom does not contain a spin quantum number, later suggested by the Sommerfeld group itself and developed by Pauli and others. As in previous UFT papers spin orbit coupling and many new effects of development of ECE appears with the use of the SU(2) basis and Pauli matrices. It is known from UFT325 that these orbitals in two dimensions must be the result of a quantization of a two dimensional precessing ellipse, and that will be the subject of the next note. This method is much clearer than that used by Sommerfeld himself in 1913, who did not have the benefit of Schroedinger Debye quantization (circ 1923 / 1924). Sommerfeld produced orbitals in 1913 which he communicated by letter to Einstein.


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