Gaussian Wave Packets

It’s been a little while since I’ve posted, mostly because I have an unrelated big project going on, so I’ve been focusing on trying to get that out the door.  And, I’m working on getting the twist ring inertial math to work, a laborious project since the Lagrangian equation of motion has too many variables for solving.  I’m trying to find ways to simplify.  In addition, I also have an iterative sim of the inertial response ready to go but haven’t had time to set it up and run it.  Hopefully with the other project almost done I’ll get to it this weekend.

One thought I’ve had in the meantime–many  quantum mechanics exercises involve modeling a photon with a wave packet that is described as having the Gaussian integral form.  The most basic variation of this form (Integral[Exp[-x^2]]) is a bell shaped curve with amplitude 1 at zero and asymptotically goes to zero at +/- infinity.  I’ve had lots of lectures where an oscillating squiggle is used to represent the magnitude of the quantized photon wave packet.

A very interesting thought occurred to me is that this integral is a great representation of the unitary twist version of a photon packet.  A one dimensional magnitude projection of a twist from the Unitary Twist Field Theory would be represented exactly by a Gaussian curve, and if we use a complex value r to completely represent the twist function, then the Gaussian integral becomes Integral[Exp[-r^2]] and then this can be interpreted as a working model of twists–and thus support the notion that the twist theory has a well proven basis in the math of quantum mechanics.  Do I buy that, or should my skepticism meter be dinging my thinking process?  Right now, the idea looks pretty workable–it seems pretty clear that the r form clearly would represent a twist as well as a Gaussian envelope packet over a frequency of oscillation of E and B fields–making the twist theory a viable alternative to the magnitude constrained wave packet interpretation.  For the twist theory to be acceptable, there has to be a path to the math of quantum mechanics, and I think I see how this could happen.



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