# What are the solutions to this equation called?

• Labyrinth
In summary, the conversation is about a specific equation involving partial derivatives and various constants. The speaker mentions the use of Spherical Bessel functions and possibly Hermite polynomials in finding solutions for this equation. The other person is unsure of a term mentioned by the speaker, which turns out to be Gegenbauer polynomials.

#### 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.

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

Bystander said:
"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.

"eigen value(s)"

Bystander said:
"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".