0

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?

Qmechanic
  • 201,751
Tsangares
  • 712

1 Answers1

1

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.

Related Solving The Radial Equation

Community
  • 1
  • Thank you all and the comments. Not a textbook, my professor makes problems. I greatly appreciate the assistance. – Tsangares Nov 10 '16 at 17:03
  • No problem. Actually, there are two Youtube video series of lectures that could be of interest to you, and you can see this from another angle. 1. James Binney (Oxford) 2. L.Susskind (Stanford). They both go through the standard course of quantum mechanics pretty well. –  Nov 10 '16 at 17:56