### Quantum Harmonic Oscillator Problem**Question:**Using the eigenvectors of the quantum harmonic oscillator, i.e., $|n\rangle$, find the matrix element $\langle 11|P|10 \rangle$, where $P$ is the momentum operator.**Options:**1. $\large i \sqrt{\frac{11m\omega \hbar}{2}}$2. $\large i \sqrt{\frac{9m\omega \hbar}{2}}$3. $\large i \sqrt{5m\omega \hbar}$4. $\large i \sqrt{6m\omega \hbar}$**Explanation:**In this problem, you are asked to compute a specific matrix element of the momentum operator $P$ between two eigenstates $|11\rangle$ and $|10\rangle$ of the quantum harmonic oscillator.The options provide different expressions involving the mass $m$, the angular frequency $\omega$, and the reduced Planck constant $\hbar$. Each expression also contains the imaginary unit $i$ and a square root. The task is to determine which of these expressions correctly represents the matrix element $\langle 11|P|10 \rangle$.This problem is a typical exercise in quantum mechanics involving the use of ladder operators and the properties of harmonic oscillator eigenstates.

Answered: Using the eigenvectors of the quantum…

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Using the eigenvectors of the quantum harmonic oscillator, i.e., |n >, find the matrix element < 11|P|10 >,where P is the momentum operator. 11mwħ 9mwh 2 O iv5mwħ O iv6mwħ о