Why is a QM wave function not normalizable

[Ed Quanta]

In quantum mechanics, why is a wave function not normalizable if it always has the same sign as its second derivative?

 

[Meir Achuz]

In 1D, if f"/f is positive, the function curves away from the x axis.
To be normalizable, it must in some region curve toward the x axis.

 

[dextercioby]

In quantum mechanics, why is a wave function not normalizable if it always has the same sign as its second derivative?

Your question doesn't make (too much) sense, since a wave function is a complex (generally with a nonzero imaginary part) valued function and to say that $a+ib >0$ makes no sense.