# Why must $\Psi (x,t)$ go to zero faster than $\frac{1}{\sqrt{|x|}}$?

Otherwise one could eventually bound the integral by $1/x$, which diverges to infinity as $\ln(x)$, and the function could not be normalized. Ofcourse, there is nothing special about $1/\sqrt{|x|}$, he could equally well have chosen $1/\sqrt{|x\ln(x)|}$. And in case you were wondering, there is no function, such that all eventually slower growing functions converge, and all faster growing functions diverge.