I have N particles of spin $\frac{1}{2}$ and I know all of them are in the ground state, in an infinite potential well ( box $1-D$).

I have to find the energy of ground state . also when $N \to \infty$.

I can do this exercise with two particles, but with infinite, I'm not sure.

So the eingenvalues of single particle are $\frac {\hbar^2 \pi^2 n^2}{2ma^2}$.

If I add all of them I obtain $\infty$. I think I'm just confused at the moment.

Thnks in advance.

  • 1
    $\begingroup$ It sounds like you may have misunderstood your assignment to me. $\endgroup$
    – J. Murray
    Jun 18 at 3:18
  • $\begingroup$ it is not possible to construct a fermionic state with more than 2 particles in the ground state of a 1d system. Something is wrong with the question or your reading of the question. $\endgroup$ 2 days ago
  • $\begingroup$ I think there's an error in the question in the exam trace. I think it just asks me what should it be the lowest energy state with $N$ fermions forced to be in $ |+>$ . In that case, is it correct to say that the energy is simply $E_1 + E_2 + ... + E_N$ and that when $N \to \infty$ the energy is simply $\infty$? $\endgroup$
    – Shanks Red
    2 days ago


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