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Operator representation of p in x basis.

  1. Aug 13, 2004 #1
    For the Schrodinger equation for a hydrogen atom, we need to write out:

    p^2/2m for the electron.

    If we define our basis states to be a linear discrete array of points, let's say 4 points. 0,d,2d, and 3d, where is some distance, on the order of a Bohr radius. How do I write p as an operator in that positional basis? I kind of have an idea of how to do it, but I don't want to say anything to bias your answers. I'll hear your ideas then tell you what I did.
  2. jcsd
  3. Aug 13, 2004 #2
    Basically I want to write this in operator notation where I have defined the basis states.

    [tex]\hat{H} = \frac{1}{2m} \hat{p}_{1}^2 - \frac{1}{4 \pi \epsilon_0} \frac{Z e}{\hat{r}_{1} - R}[/tex]
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