1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    the hamiltonian of this problem is given by

    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?

  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].
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook