## Related questions with answers

Question

Write solutions to the Schrodinger equation appropriate in the various regions, impose required continuity conditions, and obtain the energy quantization condition: $\sqrt{E} \cot \left(\frac{\sqrt{2 m E}}{\hbar} L\right)=-\sqrt{U_{0}-E}$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 6$\textbf{Concept: }$

By combining all the cases in 3 regions, we get:

$\begin{align*} \Psi(x) &= 0 \hspace {4.3cm} (x<0) \\ \Psi(x) &= A \sin{(kx)} + B \cos{(kx)} \hspace{0.75cm} (0<x<L) \\ \Psi(x) &= Ce^{-ax} \hspace{3.5cm} (x>L) \\ \end{align*}$

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