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Statistical thermodynamics: number of states of particle in central potential

  1. Apr 16, 2010 #1
    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
     
  2. jcsd
  3. Apr 16, 2010 #2
    It is asking for the number of states [tex]\Phi(E)[/tex], so it seems to be energy dependent. I believe they want the number of states below the energy [tex]E[/tex].
     
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