(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I was reviewing some homework problems and looking at the solutions. There is one problem with a tiny step I just cannot rationalize and I am hoping someone can point me in the right direction.

I have a spherical finite well:

[tex] V = {- V_{0}: 0 < r < a}[/tex],

[tex] = {0: r \geq a} [/tex]

[tex]- k_{2} = k_{1} cot (k_{1} a)[/tex] (1)

Refining the notation,

[tex]\alpha = a \sqrt{(2m(E + V_{0})}/hbar = k_{1} a[/tex]

[tex]R = a \sqrt{(2m(V_{0})}/hbar[/tex] and [tex]k_{2} = \sqrt{(2m(V_{0})}/hbar[/tex]

So (1) may be rewritten as [tex] \sqrt{R^{2} - \alpha^{2}} = - \alpha cot (\alpha)[/tex]

2. Relevant equations

From part 1.

3. The attempt at a solution

I don't understand how at [tex] R = \pi/2 [/tex] there are no bound states.

Also, I am given this restriction: [tex] -V_{0} < E < 0 [/tex]

How is this justified and how is the precise range of bound states determined?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Exam preparation question

**Physics Forums | Science Articles, Homework Help, Discussion**