- #1

BOAS

- 555

- 19

in my QM class we arrived at the expression ##\langle \hat{H} \rangle = \Sigma_{even n} |C_n|^2 E_n = \frac{24}{n^2 \pi^2} \frac{\hbar^2}{2m} \frac{n^2 \pi^2}{L^2}##.

The n terms cancel and we are left with ##\langle \hat{H} \rangle = \frac{12 \hbar^2}{mL^2} \Sigma_{even n} 1##.

My lecturer said that this sum is infinity, since the number of even integers is infinity. Why is this the case when there are no n terms for the sum to act upon?

##\Sigma_{even n} n = \infty##, but I don't understand why ##\Sigma_{even n} 1 = \infty##