H of Quantum. The Hamiltonian.

This lecture video is in regards of the Hamiltonian, the H of quantum mechanics. It will be discussed about the role of the Hamiltonian for expectation values, for time dependent systems which evolve over time and to construct a time evolving operator.

Applications used to make this lecture is listed down below.
-Cinema 4D with Python integration.
-Adobe After Effects.
-Adobe Photoshop.
-LateX.
-Audacity.

It has been a year since I have uploaded a video, seems like I make a video a year. However I will be changing my schedule a little, and will be trying to upload more content as while I was away the channel grew a ton. I have revised the channel logo and aesthetic, updating the profile picture and banner with the new version of the logo.

0:10 Expectation value
03:58 Time evolution

[Semispecula]

*PDF of this video in terms of an article can be found in the description.*

This video might be technical in contrast to a broader YouTube audience. However I want to both upload videos which is meant for a broader audience and also technical ones which is meant to reach a certain audience. Many 'popular science' videos in terms of maths and physics can be found on the platform. So I will aim for a little more technical audience in some of my videos, including this one.

Another addition: I have stopped adding music to the video background due to previous criticism. I used to put the music which I have made in the background, now I have only put a composition in the beginning and while the transitions are taking place.

[sebastiangudino]

I would like it if at 5:13 you expanded on the fact that what's sorta hapening is we are taking the exponential funciton of an operator! This is a powerful concept! And 3B1B did already a pretty cool video about exp() of a matrix. So you could dig a little deeper into that idea! After all, it IS an aproachable concept!

[aminkhodadadi]

Simply perfect. Thank you.
Thanks also for the PDF-file.
P.S. composition is icing on the cake

[thomasolson]

t_0 looks like a move to the right. hbar puts a 2pi into the numerator. Suggesting this whole thing has a period. The negative puts e into the denominator. Is h-hat spitting out its own imaginary value? If it does, the negative cancels and this whole thing turns into a tangent half angle function. Not sure what it does if it's a complex number with real and imaginary parts though. Or what happens if this h-hat thing is a polynomial.
This Hamiltonion guy must be a "🎶🎷🎵smooth operator🎶🎷🎵"