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Here is the whole problem, I understand the context... but I never encountered this notation before. It looks like set notation but it is not defining a set of real numbers.

Problem: Writing the radial wave function, $R(r)=\frac{u(r]}{r}$, show that the radial equation becomes: \begin{align} -\frac{\hbar^2}{2m}\frac{d^2 u}{dr^2} + \left[ V(r) + \frac{\hbar^2 \ell (\ell + 1)}{2mr^2}\right]u = Eu \end{align} Compare this with the one dimensional Schrodinger equation. What's similar, what's different?

Question: How do I start this problem? Specifically, what is the notation in the prompt?

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How do I start this problem? Specifically, what is the notation in the prompt.

As noted in the comments, it's a typo, it should be $R (r) = \frac {u (r)}{r} $, or you might see it written as $R_{nl}(r) = \frac {1}{r}U_{nl}(r) $ which allows for the different combinations of energy level $n $ and angular momentum $l $.

Compare this with the one dimensional Schrodinger equation. What's similar, what's different?

$$\begin{align} -\frac{\hbar^2}{2m}\frac{d^2 u}{dr^2} + \left[ V(r) + \frac{\hbar^2 \ell (\ell + 1)}{2mr^2}\right]u = Eu \end{align}$$

What's different is the effective potentential term $$V (r) +\frac{\hbar^2 \ell (\ell + 1)}{2mr^2}$$.

If your book is noticeably high on typos, you might need another source, as there are lots of substitions and rearranging to follow to solve this.

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