Connecting classical and quantum physics

Are we just gonna quietly ignore the fantastic Taylor Swift references? This is not even the first time Taylor Swift references have appeared in these videos and I am loving it!

Not to demean other yt scientists, but i think youtubers like this who actually go into the more advanced, more detailed parts of science, should deserve more views. These kinds of videos is for the more curious, those who want to know more. While other channels simplify their content quite a lot so that their viewers can understand, and i don't blame both groups of people, but i wish there are more channels like yours which wont be nerfed by the size of viewers' knowledge base. Keep it up!

I was not expecting my black and white -sometimes yellow-, physics history channel to put a colorful sponsor section in the middle of the video. Totally spooked me out, anyway good to see you're getting places with this channel.

Hey I am a high school student who loves to learn about physics and I have found videos extremely entertaining and easy to understand. Please continue do more, Thank you

Ever since I started watching your videos, every time more content is posted my interest in studying Quantum Mechanics and its history is rekindled. Even though my academic routine distances me from studying more physics, I get brought back to the subject, and I am absolutely grateful for the quality of the videos because they are second to none in peaking my interest.

Such an important story in Physics.. Awesome to see it covered with a lot of details well done!

2:14 here it is! Was I the only one to guess it correctly from the community posts?

This guy makes my day happier. Perfect video for a lazy Sunday afternoon.

That's worth a coffee and a bagel

Interesting to note that Maxwell's formula for the frequency of an orbiting, radiating electron works without a transition between states (it's stationary?), unlike the Bohr model counterpart. I see that Bohr's move of taking the limit of large quantum number N cleverly reconciles the two cases because as N gets larger the gap between levels gets smaller, so at very large N it's as if the transition isn't there and the electron just radiates while orbiting.

Still the most valuable channel on all of YouTube currently. Please keep them coming!

The mathematics is really necessary, it gives us a holistic justification to how scientists arrived to their results.

Lovely sunday, chilling after a workout and watching your wonderful video. Thank you for satisfying my need for historical stories of physics.

My goodness, this is absolutely beautiful.

Great video. Bohr's approach is fascinating. In here the circular motion of the electtron is brought to a straight movement.

Has a mathematician I really find it hard to grasp these taylor series approximations because they seem so arbitrary and without rigour, but even worse, a lot of times they can be very easily explained by studying limits! In the case of 4:20, for example, that's just the limit of x/(e^x-1) -> 1 when x ->0, where x=hv/(kt). To get that limit in that equation, because we only have 1/(e^x-1), we just multiply and divide by x to get the result. Same with 6:40. We have (x^2)*(e^x)/(e^x-1)^2 whose limit as x approaches 0 is also easy to calculate to be 1 without any taylor approximations as a simple limit. And the same in 9:44. N(1-1/(1+1/N)^2) can be simplified to (2+1/N)/(1+2/N+1/N^2) which of course approaches 2 as N approaches infinity. No need to make dubious and arbitrary approximation, and much easier to understand and also replicate in other problems. Also I really enjoy your content btw

...I geuss this is why all the most complex problems are at molecular/microbiological scale. Think about it. If we start with "simple" quantum rules at atomic level on the one end and only observe quantum rules at their limits in macroscopis scale (our everyday scale), then there is a point were rules of quatum world become most convoluted (there are just enough atoms in the observed system that ALL the interacting effects must be calculated precisely)... P.S. Awesome video as always...:)

I always believed the Correspondence Principie on faith, and always wondered how it could be demonstrated mathematically. I never understood until now. Thanks for that.

I wonder if he plans on telling how the quantum theoretical picture came to be, it would be quite enlightening to see what inspired Schrödinger, Dirac and other to come up with such an elegant framework to explain quantum phenomena.

It is a good day when JK0 uploads a video! Especially on a sunday morning!:)