Agemoz's Physics Blog

UPDATE 1: no more ads here!

UPDATE 2: There appear to be no time independent bounded eigenstates for the u,d,u (proton charge model Schroedinger equation) even when offset from the in-line axis of the particles.

(original post:) In the last post, I said that no time independent solution for the three particle u,d,u (proton charge model) Schroedinger equation was possible along the in-line axis of the particles. This is still true, however, I realized that it is still possible–in fact now is looking likely–that there is a valid time independent solution for the whole system. There actually is a valid solution along the axis, but it has to be degenerate–Psi is all zero here. I realized, however, that off-axis Psi probability can be non-zero. The analogous situation is the hydrogen orbitals above the S orbital. All of these have zero Psi at the origin, but valid (non-zero) time independent probability amplitudes everywhere else.

I’ve further enhanced the differential solver to more easily obtain the time evolved reconstructions of the Schroedinger eigenstates for the u,d,u case and other investigations. The solver will now automatically hunt for and lock onto bounded solutions, quickly identifying the eigenstates near each energy level. And, it does the Fourier transform, reconstruction, and time evolution–playback of the reconstruction is pretty fun to watch.

Here is an arbitrarily complicated quantum well demonstration: red is the quantum well, the yellow line is the current energy level (a bound eigenstate is shown), green is Psi (the probability amplitude), blue is the second derivative, gray is the rate of change of Psi. In the lower left are the sine and cosine frequencies generated by the Fourier transform of Psi, and the lower right orange curve is the time evolved reconstruction of Psi at some later time t.

I’ll have the proton charge model results up shortly.

Agemoz

UPDATE: I saw that horrible obnoxious wordpress advertising, yeeechhh! When I look at my own posts, I don’t see them, but when I used another device to view this site, I just barfed, it is so bad. I just went on a paid plan so you don’t have to see that crap.

Tags: physics, quantum, quantum theory, special relativity

This entry was posted on August 6, 2022 at 12:26 am and is filed under Physics. You can follow any responses to this entry through the RSS 2.0 feed. You can skip to the end and leave a response. Pinging is currently not allowed.