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Schroedinger Wave Equation #135

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Schroedinger Wave Equation #135

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lukem12345
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@lukem12345 lukem12345 commented Jul 29, 2023

There is some interest in Decapodes for applications concerning quantum mechanics. There is interest in Decapodes for which differential forms are complex-valued.

This PR will allow users to specify using of Complex over Float input data, and provide an example of the Schroedinger Wave Equation written as a Decapode.

schroedinger
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schroedinger

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lukem12345 commented Aug 4, 2023

It was suggested by @NOTtheMessiah that there may be some good initial conditions to be found here: http://www.falstad.com/qm1d/

@lukem12345 lukem12345 self-assigned this Aug 10, 2023
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TODO: Plot magnitude as the probability amplitude and LGTM

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Here is the plot using the extrema of |Psi|*|Psi| at each time step.
According to some quick reading, it is expected for Psi to go to infinity unless given "exactly the right initial conditions".
https://galileo.phys.virginia.edu/classes/751.mf1i.fall02/OneDimSchr.htm

So, this PR will be good to merge once we update it to use the appropriate method of specifying ComplexF64 as the type.

schroedinger_abs_wedge

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