436(4) : General Solution of the Schroedinger Equation

Interesting discussion. It becomes clear that computational quantum chemistry packages can be modified with t goes to m(r) power half t and r goes to r / m(r) half in the wavefunction. In general all the ideas of UFT415 ff. can be developed with computational quantum chemistry. In the IBM Clementi environment the LCAP system was used with the IBM 3096 and IBM 3084. These systems were also used at the Cornell Theory Center. I think that these computations can now be carried out on desktops. In the first instance it would be very interesting to compute the Lamb shift for 2S sub 1 / 2 to 2P sub 1/2 in atomic H and adjust m(r) for exact agreement with the data. These are known now with great precision.

Doug,

the spin connection seems to play a similar role as the so-called exchange-correlation potential in N-electron calculations. Perhaps there is a connection. Also the N-electron calculations have to be performed iteratively until a convergence is obtained, i.e. the new electron potential from your eq. (46) leads to the original total potential entering the solution of the Schrödinger equation.

Horst

Am 08.04.2019 um 17:44 schrieb Doug Lindstrom:

Horst:
I’ve attached a pdf version which opened on my computer okay. The doc file was corrupt. As far as I remember, the potential was periodic up to the first Bohr orbit.
Doug

On Apr 8, 2019, at 7:53 AM, Horst Eckardt <mail> wrote:

Doug,

I cannot open the Word document. Besides this, did you apply a periodic potential of infinite length? Normaly the charge density as well as the atomic potential have to go to zero for r –> infinity.

Horst

Am 08.04.2019 um 16:47 schrieb Doug Lindstrom:

This is somewhat similar to the structure of the hydrogen atom computed for the Serbian talk back in 2010 (paper attached), which is reassuring. Figure 1 for the electron potential has a minimum near r=0.1 and a max around r=0.5 for kappa = 2 Pi (orange).
On Apr 7, 2019, at 9:41 PM, Myron Evans <myronevans123 wrote: Computation of the Valence Charge Density of the Nickel Atom This is an exceedingly interesting development, this program applies computational quantum chemistry to the m theory and finds an effect on the valence structure of the nickel atom. It is a small effect as expected, but nevertheless it is a real effect, similar to the Lamb shift, also a small effect. So the generally relativistic quantum mechanics can be coded up in computational quantum chemistry, and applied to a vast number of problems. This program can be used to develop the m theory far in advance of analytical solutions of the Schroedinger equation. The latter is analytical only for the H atom, as is well known. For the helium atom onwards, computational methods have to be used. It would be interesting to apply this program to a proton interacting with the nickel atom, using m theory. That might lead to low energy nuclear reaction. I think that thi sis a big step forward and this program can be used in many ways. The effect of m space is that the wave functions psi(r) are shifted to the outer region by psi(r) --> psi( r/sqrt(m(r)) ) because r/sqrt(m(r)) >= r. I succeeded in reactivating an old electronic structure program for atoms which a colleague at the TU Clausthal sent me years ago. I calculated the charge density of a Ni atom. The valence charge density (10 electrons) is graphed in the file, in original form and with shifted radius coordinate as above. One has to make the parameter R of the m function quite large to find a visible effect. I hope that jpg files go through the wordpress upload better than png files. Horst Am 07.04.2019 um 09:31 schrieb Myron Evans:
436(4) : General Solution of the Schroedinger Equation This is given by Eq. (8) and several examples given. In the usual vacuum free quantum mechanics the expectation value of energy from Eq. (8) is given by <E> = E, but in quantum mechanics in m space (or the vacuum), i.e. generally covariant quantum mechanics, the energy levels are shifted according to Eq. (31). This is a general law of quantum mechanics, true for any spectral line.
<rhoval-Ni.jpg>

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