# Energy of infinite number of particles in a box [closed]

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.

• 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 $\infty$? 2 days ago