Chapter 7, Problem 29P

Which one of the following functions, and why, qualifies to be a wave function of a particle that can move along the entire real axis?

1. $\psi \left(x\right)=Ae-x^2;$

$\psi \left(x\right)=A{e}^{-x};$

$\psi \left(x\right)=A\tan x;$

$\psi \left(x\right)=A\left(\sin x\right)/x;$

$\psi \left(x\right)=A{e}^{-\left|x\right|}$