3.5.5.1 So­lu­tion piped-a

Ques­tion:

Write down eigen­func­tion num­ber 6.

An­swer:

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

$$\psi_n = \sqrt{\frac{2}{\ell_x}} \sin\left(\frac{n\pi}{\ell_x} x\right)$$

you get

$$\psi_6 = \sqrt{\frac{2}{\ell_x}} \sin\left(\frac{6\pi}{\ell_x} x\right)$$