Question
Prove that the function $\psi=A e^{i k x}+B e^{-i k x}$ satisfies the equation $\psi^{\prime \prime}=-k^{2} \psi$ for any two constants $A$ and $B$.
Step 1
The derivative of $e^{i k x}$ is $i k e^{i k x}$ and the derivative of $e^{-i k x}$ is $-i k e^{-i k x}$. So, the first derivative of the function $\psi$ is: \[\psi^{\prime}=i k A e^{i k x}-i k B e^{-i k x}\] Show more…
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