Chapter 40, Problem 40.44P

(a)

To determine

The wave function $\psi \left(x\right)={\displaystyle {\int }_0^{\infty }B\left(k\right)\cos kxdk}$ for the function $B\left(k\right)=\left\{\begin{array}{l}0k<0\\ \frac{1}{k_0},0\le k\le k_0\\ 0,k>k_0\end{array}\right\}$.

(b)

To determine

To plot: The graph of $B\left(k\right)$ versus $k$ as well as $\psi \left(x\right)$ versus $x$ for $k_0$ is $\frac{2\pi }{L}$. and locate the points at which $\psi \left(x\right)$ is zero and the width $w_x$ of the wave function on $\psi \left(x\right)$ versus $x$ graph.

(c)

To determine

To plot: The graph of $B\left(k\right)$ versus $k$ as well as $\psi \left(x\right)$ versus $x$ for $k_0$ is $\frac{\pi }{L}$ and locate the points at which $\psi \left(x\right)$ is zero and the width $w_x$ of the wave function on $\psi \left(x\right)$ versus $x$ graph.

(d)

To determine

Product $w_p{w}_x$ and compare to the Heisenberg uncertainty principle.