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Quantum wave packet 3D model

Posted 3 years ago

Hello everyone. I've been using Mathematica to model basic Quantum Mechanics functions. Pretty having fun with it as I learn. I'm trying to see if I'm able to publish the plots properly, and I'm happy to engage in open discussion about the Wave Packet. It'll be a good check on learning.

POSTED BY: John Baxter

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

POSTED BY: Ozan Yarman
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