I agree with you.
In my opinion ## k = {\pi}/{a}## (condition satisfied in the reciprocal space) means that there will be two standing waves (## \psi(+) \text{ and } \psi(-)##) along the direct space, as you can see in your second figure.
Hello everybody.
I'm a Telecommunication Engineer with more than 25 years of experience, currently finishing a Bsc in physics.
I've some problems with my english but I hope it won't be a problem in parcitcipate. Be patient with me.
Thanks in advance.