Chapter 40, Problem 40.53P

(a)

To determine

To plot: The graph between the wave function and distance.

(b)

To determine

To show: Whether the wave function $\psi \left(x\right)=\{\begin{array}{l}{e}^{+\kappa x},x<0\\ e^{-\kappa x},x\ge 0\end{array}$ satisfies the Schrodinger equation for $x<0$ if the energy is $E=-\frac{{\hslash }^2{\kappa }^2}{2m}$ .

(c)

To determine

To show: Whether the wave function $\psi \left(x\right)=\{\begin{array}{l}{e}^{+\kappa x},x<0\\ e^{-\kappa x},x\ge 0\end{array}$ satisfies the Schrodinger equation for $x\ge 0$ if the energy is $E=-\frac{{\hslash }^2{\kappa }^2}{2m}$.

(d)

To determine

Why the wave function $\psi \left(x\right)=\{\begin{array}{l}{e}^{+\kappa x},x<0\\ e^{-\kappa x},x\ge 0\end{array}$ is not an acceptable wave function.