Agemoz's Physics Blog

I try to post rarely, usually after some new learning in my research studies. In the last few days I’ve posted about the interesting results from my iterative differential equation solver, and that’s enough for now. However, I tried something new and was fascinated by the result, so I felt like I had to do one more post that demonstrated the power of the differential solver, and then will head back to my studies. I don’t get the sense that anybody reads these, and the purpose of this blog is mostly for my research study journalling, so hopefully no harm done.

Yesterday, I posted how the differential equation solver was yielding results that match expected solutions to various Schroedinger time independent equations, and showed how it is identifying eigenstate energies of various potential wells.

I realized that the solver would also work fine for various time dependent problems, and thought of the laser case. I set up a scenario where a flat potential well and a specific energy level creates a wave of a specific frequency. At a later time, I set up a different potential with a sine wave component added in–a setup where a photon wave travels in a region of another photon wave of a different frequency. I found that the solution phase locked to the potential sine wave. That’s not really a surprise, but what was a big surprise is that this lock was independent of the energy of the system or the average depth of the well, both of which normally set the oscillation frequency of psi. The change in potential is a sine wave in this case, and that always caused a phase lock to the potential well frequency regardless of the depth of the potential well OR the energy of the system!

I’m going to try to find the points where this behavior breaks and the depth of the well or the energy level dominate the psi oscillation frequency. I also have to think if this test setup really mimics what happens in a laser, I kind of have my doubts. Nevertheless, some really interesting results!

agemoz

Tags: physics, quantum, special relativity

This entry was posted on July 23, 2022 at 9:43 pm 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.