3.5.5.2 So­lu­tion piped-b

Ques­tion:

Write down eigen­value num­ber 6.

An­swer:

Sub­sti­tut­ing $n$ $\vphantom0\raisebox{1.5pt}{$=$}$ 6 in the generic ex­pres­sion for the eigen­val­ues,

$$E_n = \frac{n^2\hbar^2\pi^2}{2m\ell_x^2}$$

you get

$$E_6 = \frac{36\hbar^2\pi^2}{2m\ell_x^2}$$