Wave-function solution of a rectangular-well potential

[Happiness]

Is the solution given below wrong?

I believe the $x$ in (25.2) is wrong; it should be replaced by a constant, such as $\beta$, because $E$ is a constant and not dependent on $x$.

Should the correct answer be
even solution:

odd solution:

where

 

[PietKuip]

That is not an x but the greek letter kappa.

 

[Happiness]

That is not an x but the greek letter kappa.

I could hardly tell the difference!

 

[jtbell]

That is a terrible typeface. I've never seen a kappa that looks like that!

 

[nrqed]

That is not an x but the greek letter kappa.

To me it looks much more like the Hebrew letter aleph...