7.1 Exercise 11

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? (a) $\psi \left(x\right) = A e^{− x^{\textrm{ } 2}}$;
(b) $\psi \left(x\right) = A e^{− x}$; (c) $\psi \left(x\right) = A \text{tan} x$;
(d) $\psi \left(x\right) = A \left(\right. \text{sin} x \left.\right) / x$; (e) $\psi \left(x\right) = A e^{− \left|x\right|}$.