What are the solutions to this equation called?

[Labyrinth]

$$\frac{-\hbar}{2m} \frac {\partial^2\psi(r)} {\partial r^2} + \frac {\hbar^2l(l+1)}{2m} \frac {\psi(r)}{r^2}+v(r)\psi(r)= E \psi(r)$$

It's seen in this part of a Susskind video lecture.

He mentions some kind of polynomial or function that I don't recognize for the solutions. He says to look it up and I would love to but I'm unable to make out what he said. Any ideas?

Thank you for your time.

 

[Bystander]

"Spherical Bessel functions." May also have been a mention of Hermite polynomials.

 

[Labyrinth]

"Spherical Bessel functions." May also have been a mention of Hermite polynomials.

Thanks for the quick reply. Will check those out.

He says something that sounds like "giggenval", but I cannot find any reference to something that sounds like that.

 

[Bystander]

"eigen value(s)"

 

[Labyrinth]

"eigen value(s)"

Nah, he says that all the time, and there's definitely no 'you' sound at the end. It's like "vaul" or "vaula".

 

[HallsofIvy]

What he is saying is "Gegenbauer polynomials". There is a Wikipedia page at http://en.wikipedia.org/wiki/Gegenbauer_polynomials and Wolfram defines them at http://mathworld.wolfram.com/GegenbauerPolynomial.html

 

[Labyrinth]

What he is saying is "Gegenbauer polynomials". There is a Wikipedia page at http://en.wikipedia.org/wiki/Gegenbauer_polynomials and Wolfram defines them at http://mathworld.wolfram.com/GegenbauerPolynomial.html

Awesome, thanks!