Solving the Time-dependent Schrödinger Equation for the 1D Particle in a Box

[@SampleroftheMultiverse]

For those that like seeing mechanical analogs, here is on your have not seen. kzbin.info/www/bejne/raOlpKSfepWpfZYsi=waT8lY2iX-wJdjO3 The video is one of two mechanical method to quantizing a system. It has been used to produce stable structures that are basically trusses. Area under a curve is often equivalent or represents energy. Buckling of sheet of flat material representing a field shows a very rapid growth of area. If my model applies, it may show how the universe’s energy naturally developed from the inherent behavior of fields. Under the right conditions, the quantization of a field is easily produced. The ground state energy is induced via Euler’s Contain Column effect. Containing the column must come in to play before over-buckling, or the effect will not work. The sheet of elastic material “system” response in a quantized manor when force is applied in the perpendicular direction. Adjoining the points of highest probabilities ( ie peeks and troughs) to a top and bottom sheet produced the stable structure.

[@Illumiscardepp]

I am tyro of quantum field, and this video help me explicate the entire process of deprivation, thanks alot! I learn my-self 4h to solve my tutorial question, but get nothing🤧. But thanks to this video, i totally comprehend it!!!!

[@GianmarcGrazioliPhD]

I am so glad that my video was helpful, thank you very much for your message!

[@czyes]

I don't usually leave comments but man, this video is absolute gold! the explanation is super clear, I understood all the math but the final part, where you talk about the superposition and linear combination of two states, but I think that is because I don't know the theory well enough... I have one question though: how much harder is solving the equation for 2 charged particles in 1D box? In that case the potential is time dependent because the charged particles effect each others so you can't separate the variables I think... I'd like to solve that but I don't know if my math can handle it XD

[@GianmarcGrazioliPhD]

Thanks a lot! You are correct that the total potential would become time-dependent with two interacting charged particles in a 1D box, and the problem would become much more difficult to solve! 🙂 I found two papers where it looks like the authors are doing something like this: www.degruyter.com/document/doi/10.2478/s11534-006-0005-2/html here is the earlier paper: arxiv.org/pdf/physics/9909042.pdf

[@czyes]

@@GianmarcGrazioliPhD Thank you so much for the answer :D I'll check both papers thanks!

[@sevans3600]

This video is incredible. Thank you so much for this.

[@GianmarcGrazioliPhD]

Thank you so much! 🙂

[@ioannaathineos5269]

Just amazing !!Thank you so much💯

[@GianmarcGrazioliPhD]

Thanks a lot! :-)

[@trickytn2322]

This is gold, thank you so much Dr❤

[@GianmarcGrazioliPhD]

I’m so glad it was helpful! You're most welcome, and thanks for your note 🙂