Evaluate , , △x, △px, and △x△px for the provided normalized wave function
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Evaluate <x>, <px>, △x, △px, and △x△px for the provided normalized wave function.
![The function \( \Psi(x) \) is defined as follows:
\[
\Psi(x) =
\begin{cases}
\sqrt{\frac{2}{L}} \sin \frac{\pi x}{L} & \text{for } 0 < x < L \\
0 & \text{elsewhere}
\end{cases}
\]
This equation describes a wave function, typically used in quantum mechanics, for a particle in a one-dimensional box with boundaries at \( x = 0 \) and \( x = L \). The function is sinusoidal within these boundaries and zero elsewhere, indicating the particle has zero probability of being found outside the interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F772ba77e-5b00-472d-814c-750947c36afa%2Fb9eee9a1-3bbe-42b6-a072-11d8b8b5b236%2Fy3cm4xk_processed.png&w=3840&q=75)
Transcribed Image Text:The function \( \Psi(x) \) is defined as follows:
\[
\Psi(x) =
\begin{cases}
\sqrt{\frac{2}{L}} \sin \frac{\pi x}{L} & \text{for } 0 < x < L \\
0 & \text{elsewhere}
\end{cases}
\]
This equation describes a wave function, typically used in quantum mechanics, for a particle in a one-dimensional box with boundaries at \( x = 0 \) and \( x = L \). The function is sinusoidal within these boundaries and zero elsewhere, indicating the particle has zero probability of being found outside the interval.
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