⁴According to the dictionary mentioned in the previous section, for a potential well where x ∈ [− L ∕2,L ∕2] the dimensionless position variable has been chosen to be x∕(L∕2) ∈ [− 1,1] . Then ℏ2
En = 2m(L∕2)2𝜖n ℏ2π2 2
= 2mL2-n and (+) ∘ ----
ψ n (x) = 2∕L cos(nπx ∕L) , ∘ ----
ψ (−n)(x) = 2∕L sin(nπx∕L ) . Note that 𝜖n = p2n according to equations (10.13) and (10.14) .