Superb. Pure gem. I am speechless. In 9 and a half minutes this video sums up at least an entire chapter worth of mathematical methods text in Physics. I have yet to come across a material this concise and yet in depth enough
A small correction: the operator L you defined is symmetric, not necessarily self-adjoint. For this you would either have to show that L is bounded or that the domain of L coincides with the domain of L*
I would love a similar video for other sets of orthogonal functions. As well as a unified overview of techniques that work for many such sets of functions. They usually are orthogonal with respect to some scalar product, they are solutions to some kind of differential equation(eigenfunctions of some differential operator) and so on Even though I knew everything presented in the video, I really like the way it is structured. Deep enough, but consise.
You're right, there should have been a (-1)^n. In generally adapted the approach in math.stackexchange.com/questions/4941449/derivation-of-legendre-polynomials-from-only-orthogonality and the filled in the details.
Superb. Pure gem. I am speechless. In 9 and a half minutes this video sums up at least an entire chapter worth of mathematical methods text in Physics. I have yet to come across a material this concise and yet in depth enough
Thank you for not oversimplifying things! Would be cool to include more examples of these used in physics
World class quality! My compliments.
your channel has been a goldmine for me, amazing explanations and the graphics are suburb.
This channel is pure gold!!
A small correction: the operator L you defined is symmetric, not necessarily self-adjoint. For this you would either have to show that L is bounded or that the domain of L coincides with the domain of L*
I would love for this to be stressed more often. Physics professors usually gloss over the difference
Wonderful channel ! So clear and efficient
Is anyone else dizzy, or it's just me.
I could benefit from a longer video
Amazing video! I look forward to what you will post next!
I would love a similar video for other sets of orthogonal functions. As well as a unified overview of techniques that work for many such sets of functions. They usually are orthogonal with respect to some scalar product, they are solutions to some kind of differential equation(eigenfunctions of some differential operator) and so on
Even though I knew everything presented in the video, I really like the way it is structured. Deep enough, but consise.
Thanks again for a masterpiece, this AI voice is a major improvement!
Think you need a (-1)^n at 3:57, but it doesn't interfere with the next step. Really sleek arguments all around. What sources did you use?
You're right, there should have been a (-1)^n. In generally adapted the approach in math.stackexchange.com/questions/4941449/derivation-of-legendre-polynomials-from-only-orthogonality and the filled in the details.
Which AI voice you are using please tell.
Wish i could understand this