Hermite Differential Equation and Hermite Polynomials

In this video, I demonstrate how to solve the #HermiteODE using the #SeriesSolution method to obtain the #HermitePolynomials.

EDIT: At 1:40, I say that the derivative of the sum is the sum of the derivatives - this only applies for an infinite series if we're working within the radius of convergence. In this situation though, the radius of convergence can be infinite since the ODE doesn't have any singularities. Thanks to Quinn Kolt in the comments for pointing this out!

Questions/requests? Let me know in the comments!

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[ErwinSchrodinger]

Stationary harmonic oscillators... in terms of partial differential equations... Hermite polynomials will be involved. Anyone that's going to study Quantum Mechanics, Hermite polynomials will come into play when V(x)=harmonic oscillator or V(x, y, z... N)=N-dimensional harmonic oscillator. Thank you Faculty of Khan. My students will thank you soon. I will thank you when I teach Quantum Theory this fall.

[of_discourse]

Derivative of the sum is the sum of derivatives is only generally true when the sum is finite, but I think you can do this for any Taylor series, assuming it converges in a neighborhood of that region.

[cicerohitzschky]

Excellent class, teacher! What software do you use to write on the screen?

[mohamedjahimti]

Can you make videos on Generating Functions for Legendre, Bessel and Hermite Polynomials. It would be very helpful if you can do it ASAP

[vivekpanchal]

For physicist Hermite polynomials, why we set a0 nd a1 diffrent for each order of Hermite polynomials? I am confused whether it is done for making the wave function normalised or there is any other reason?

[lichifang]

Would you consider making a video on Mathieu function (differential equation)? Almost no video about that is available currently on youtube

[Ryze]

Could you please explain where the ODE comes in the first place? How do you derive the ODE for the processes it is meant to describe?

[anaeem]

Can u plz share as to which video editor u use

[morethanjustasloth]

"This equation will really help us in quantum mechanics."

Man I just wanna figure out what how to draw a line in GLSL.

[seanziewonzie]

Pronounced "air meet" not "her might"

[ricardoraymond]

Your subtitles are larger than your black board written characters. Very

[abublahinocuckbloho]

mate you have a way with words, you make a mountain out of a mole hill. something that can be explained in a sentence, you take a paragraph. consider "instead of having an infinite series containing the sum of a bunch of polynomial terms" how about "instead of an infinite series" instead. you might want to put your script through grammarly to avoid a lot of unnecessary waffling like you are finding words to make sure you reach a word limit. there are a bunch of other examples in this video and every other fucken video you made