Question

9.19 Show by direct operation that \[ \begin{array}{l} \hat{L}^{2} Y_{2}{ }^{2}=6 \hbar^{2} Y_{2}^{2} \\ \hat{L}_{z} Y_{2}{ }^{2}=2 \hbar Y_{2}^{2} \end{array} \]

          9.19 Show by direct operation that
\[
\begin{array}{l}
\hat{L}^{2} Y_{2}{ }^{2}=6 \hbar^{2} Y_{2}^{2} \\
\hat{L}_{z} Y_{2}{ }^{2}=2 \hbar Y_{2}^{2}
\end{array}
\]

9.19 Show by direct operation that

L̂^2 Y2^2=6 ħ^2 Y2^2
L̂z Y2^2=2 ħ Y2^2

Added by Joshua M.

Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Chapter 5

Instant Answer

Solved by Expert Frank Deng

Step 1

The operator \(\hat{L}^2\) is given by: \[ \hat{L}^2 = -\hbar^2 \left( \frac{1}{\sin \theta} \frac{\partial}{\partial \theta} \left( \sin \theta \frac{\partial}{\partial \theta} \right) + \frac{1}{\sin^2 \theta} \frac{\partial^2}{\partial \phi^2} \right) \] Show more…

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9.19 Show by direct operation that \[ \begin{array}{l} \hat{L}^{2} Y_{2}{ }^{2}=6 \hbar^{2} Y_{2}^{2} \\ \hat{L}_{z} Y_{2}{ }^{2}=2 \hbar Y_{2}^{2} \end{array} \]