Chapter A.2, Problem 9P

(a)

To determine

To Compute: The${\left|\Psi \left(x\right)\right|}^2$.

To Draw: Thesketch for ${\left|\Psi \left(x\right)\right|}^2$.

(b)

To determine

To Show:The value of $A$ to be equal to ${\left(2a/\pi \right)}^{\frac{1}{4}}$ .

(c)

To determine

To Show: The standard deviation can be expressed as $\frac{1}{2\sqrt{a}}$ .

(d)

To determine

To Show: The expression for $\tilde{\Psi }\left(k\right)$ .

To Draw:The curve for $\tilde{\Psi }\left(k\right)$ .

(e)

To determine

To Show: The expressionfor $\Delta k$.

(f)

To determine

To Calculate: The value of $\Delta p_x$ for the given wave function.

To Check:Whether uncertainty principle holds or not.