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

Give the number of states (energy of the state smaller than E<0) [tex]\Phi(E)[/tex] of a spinless particle with mass [tex]m[/tex] in the central potential [tex]V(\vec{r})=-\frac{a}{\left|\vec{r}\right|}[/tex].

2. Relevant equations

3. The attempt at a solution

Hi,

the hamiltonian of this problem is given by

[tex]\mathcal{H}=\frac{p^2}{2m}-\frac{a}{r}[/tex]

with [tex]|\vec{r}|=r[/tex]

I know, that the energy eigenvalues of such an potential can be expressed by:

[tex]E_n = -\frac{E_0}{n^2}[/tex]

where E_0 is the ground state energy.

But how do I count the number of states? Isn't the number of states that are smaller than a specific E<0 infinite?

Best,

derivator

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# Homework Help: Statistical thermodynamics: number of states of particle in central potential

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