Greetings Mr. Baxter. I am using Mathematica Home Edition 12.3. I am very interested in your code and tried to run it on my computer. While it works very well, it nevertheless gave a few errors.
<< Notation`
resulted in the following errors:
Join::incpt: Incompatible elements in Join[<|intt->RowBox[{\[Integral],RowBox[{\[SelectionPlaceholder],RowBox[{\[DifferentialD],\[Placeholder]}]}]}],dintt->RowBox[{SubsuperscriptBox[\[Integral],\[SelectionPlaceholder],\[Placeholder]],RowBox[{\[Placeholder],RowBox[{\[DifferentialD],\[Placeholder]}]}]}],rintt->RowBox[{UnderscriptBox[\[Integral],RowBox[{\[SelectionPlaceholder],\[Element],\[Placeholder]}]],\[Placeholder]}],sumt->RowBox[{UnderoverscriptBox[\[Sum],RowBox[{\[SelectionPlaceholder],=,\[Placeholder]}],\[Placeholder]],\[Placeholder]}],prodt->RowBox[{UnderoverscriptBox[\[Product],RowBox[{\[SelectionPlaceholder],=,\[Placeholder]}],\[Placeholder]],\[Placeholder]}],dt->RowBox[{SubscriptBox[\[PartialD],\[SelectionPlaceholder]],\[Placeholder]}],<<37>>,cI->TemplateBox[{},CombinatorI],cK->TemplateBox[{},CombinatorK],cS->TemplateBox[{},CombinatorS],cW->TemplateBox[{},CombinatorW],cY->TemplateBox[{},CombinatorY]|>,<<9>>,<<4>>] cannot be joined.
Join::incpt: Incompatible elements in Join[<|intt->RowBox[{\[Integral],RowBox[{\[SelectionPlaceholder],RowBox[{\[DifferentialD],\[Placeholder]}]}]}],dintt->RowBox[{SubsuperscriptBox[\[Integral],\[SelectionPlaceholder],\[Placeholder]],RowBox[{\[Placeholder],RowBox[{\[DifferentialD],\[Placeholder]}]}]}],rintt->RowBox[{UnderscriptBox[\[Integral],RowBox[{\[SelectionPlaceholder],\[Element],\[Placeholder]}]],\[Placeholder]}],sumt->RowBox[{UnderoverscriptBox[\[Sum],RowBox[{\[SelectionPlaceholder],=,\[Placeholder]}],\[Placeholder]],\[Placeholder]}],prodt->RowBox[{UnderoverscriptBox[\[Product],RowBox[{\[SelectionPlaceholder],=,\[Placeholder]}],\[Placeholder]],\[Placeholder]}],dt->RowBox[{SubscriptBox[\[PartialD],\[SelectionPlaceholder]],\[Placeholder]}],<<37>>,cI->TemplateBox[{},CombinatorI],cK->TemplateBox[{},CombinatorK],cS->TemplateBox[{},CombinatorS],cW->TemplateBox[{},CombinatorW],cY->TemplateBox[{},CombinatorY]|>,<<9>>,<<5>>] cannot be joined.
Even so, the graphs came our right.
To calibrate the wavepacket to be non-dispersive, I tweaked some values in the control box. A low mass (m) particle seems to disperse very quickly with respect time (t) regardless of its relativistic or non-relativistic velocity (V). The amplitude (
$\Delta x$e) has no bearing on this fact. However, increasing the density of the wavepacket (ke) affects the dispersiveness. By maximizing the said parameters, I was able to simulate a more or less non-dispersive propagating wavepacket.
I now have two questions:
1) Does one require to formulate a different code in order to achieve a fully correct non-dispersive 3D representation?
2) How can the two-entity gravitating photon model advanced in https://www.sciencedirect.com/science/article/abs/pii/S000349162300132X be realized? This is a new concept that allows for a quantal test object in a gravitational field to be torn apart into its constituents (viz. "pair production"). The constituents are the forefront
$hf/c^2$ and the kernel
$m$0∞e-$\alpha$> that lags behind it (with
$\alpha$ being
$GM/rc^2$).
Thank you!
Prof. Dr. Ozan Yarman
Istanbul University