Question

\begin{equation} \int_0^a \frac{1}{2} \Psi_1 \Psi_2 e^{-i(E_1 t/\hbar)} e^{i(E_2 t/\hbar)} = 0 \end{equation} $\Psi_n(x) = \begin{cases} \sqrt{\frac{2}{a}} \sin(\frac{n \pi x}{a}), & 0 < x < a, \\ 0, & \text{otherwise} \end{cases}$

          \begin{equation*}
\int_0^a \frac{1}{2} \Psi_1 \Psi_2 e^{-i(E_1 t/\hbar)} e^{i(E_2 t/\hbar)} = 0
\end{equation*}

$\Psi_n(x) = \begin{cases}
\sqrt{\frac{2}{a}} \sin(\frac{n \pi x}{a}), & 0 < x < a, \\
0, & \text{otherwise}
\end{cases}$

∫0^a (1)/(2)Ψ1 Ψ2 e^-i(E1 t/ħ) e^i(E2 t/ħ) = 0

(x) = √((2)/(a))sin((n π x)/(a)), 0 < x < a,

0, otherwise

Added by Justin P.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Ashwin Banarsee

Step 1

t/n)i(Et/n): -i(.t/n)i(Et/n) = -i(t/n) * i(Et/n) Next, let's consider the conditions for the expression to be true: Show more…

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Please show how -i(.t/n)i(Et/n) e (nT D>x>0 0, otherwise When:

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Question

\begin{equation*} \int_0^a \frac{1}{2} \Psi_1 \Psi_2 e^{-i(E_1 t/\hbar)} e^{i(E_2 t/\hbar)} = 0 \end{equation*} $\Psi_n(x) = \begin{cases} \sqrt{\frac{2}{a}} \sin(\frac{n \pi x}{a}), & 0 < x < a, \\ 0, & \text{otherwise} \end{cases}$

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\begin{equation} \int_0^a \frac{1}{2} \Psi_1 \Psi_2 e^{-i(E_1 t/\hbar)} e^{i(E_2 t/\hbar)} = 0 \end{equation} $\Psi_n(x) = \begin{cases} \sqrt{\frac{2}{a}} \sin(\frac{n \pi x}{a}), & 0 < x < a, \\ 0, & \text{otherwise} \end{cases}$